JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank

done Critical Thinking Total Questions - 67

• question_answer1)
  Two equal negative charge ? q are fixed at the fixed points \[(0,\,a)\] and \[(0,\,-a)\] on the Y-axis. A positive charge Q is released from rest at the point \[(2a,\,0)\] on the X-axis. The charge Q will [IIT 1984; Bihar MEE 1995; MP PMT 1996]
  A)
             Execute simple harmonic motion about the origin done clear
  B)
                     Move to the origin and remain at rest done clear
  C)
                     Move to infinity done clear
  D)
                     Execute oscillatory but not simple harmonic motion done clear
  View Solution play_arrow

• question_answer2)
  An electric line of force in the xy plane is given by equation \[{{x}^{2}}+{{y}^{2}}=1\]. A particle with unit positive charge, initially at rest at the point \[x=1,\ y=0\] in the \[xy\] plane          [IIT 1988]
  A)
                     Not move at all done clear
  B)
                     Will move along straight line done clear
  C)
                     Will move along the circular line of force done clear
  D)
                     Information is insufficient to draw any conclusion done clear
  View Solution play_arrow

• question_answer3)
  A positively charged ball hangs from a silk thread. We put a positive test charge \[{{q}_{0}}\]at a point and measure \[F/{{q}_{0}}\], then it can be predicted that the electric field strength \[E\] [CPMT 1990]
  A)
                     \[>F/{{q}_{0}}\] done clear
  B)
                                       \[=F/{{q}_{0}}\] done clear
  C)
                     \[<F/{{q}_{0}}\]           done clear
  D)
             Cannot be estimated done clear
  View Solution play_arrow

• question_answer4)
  A solid metallic sphere has a charge \[+\,3Q\]. Concentric with this sphere is a conducting spherical shell having charge \[-Q\]. The radius of the sphere is \[a\] and that of the spherical shell is \[b(b>a)\]. What is the electric field at a distance \[R(a<R<b)\] from the centre                                                                  [MP PMT 1995]
  A)
                     \[\frac{Q}{2\pi {{\varepsilon }_{0}}R}\] done clear
  B)
                                       \[\frac{3Q}{2\pi {{\varepsilon }_{0}}R}\] done clear
  C)
                     \[\frac{3Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]              done clear
  D)
             \[\frac{4Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\] done clear
  View Solution play_arrow

• question_answer5)
  If on the concentric hollow spheres of radii \[r\] and \[R(>r)\] the charge \[Q\] is distributed such that their surface densities are same then the potential at their common centre is  [IIT 1981; MP PMT 2003]
  A)
                     \[\frac{Q({{R}^{2}}+{{r}^{2}})}{4\pi {{\varepsilon }_{0}}(R+r)}\] done clear
  B)
                                       \[\frac{QR}{R+r}\] done clear
  C)
                     Zero                                  done clear
  D)
             \[\frac{Q(R+r)}{4\pi {{\varepsilon }_{0}}({{R}^{2}}+{{r}^{2}})}\] done clear
  View Solution play_arrow

• question_answer6)
  Two equal charges \[q\] of opposite sign separated by a distance \[2a\] constitute an electric dipole of dipole moment \[p\]. If \[P\] is a point at a distance \[r\] from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle \[\theta \] with the axis of the dipole, then the potential at \[P\] is given by \[(r>>2a)\] (Where\[p=2qa\]) [MP PET 1997]
  A)
                     \[V=\frac{p\cos \theta }{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\] done clear
  B)
                                        \[V=\frac{p\cos \theta }{4\pi {{\varepsilon }_{0}}r}\] done clear
  C)
             \[V=\frac{p\sin \theta }{4\pi {{\varepsilon }_{0}}r}\]            done clear
  D)
             \[V=\frac{p\cos \theta }{2\pi {{\varepsilon }_{0}}{{r}^{2}}}\] done clear
  View Solution play_arrow

• question_answer7)
  A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square is                                            [MP PMT 1997; AMU 1999]
  A)
             \[\frac{q}{{{\varepsilon }_{0}}}\]                                     done clear
  B)
             \[\frac{q}{\pi {{\varepsilon }_{0}}}\] done clear
  C)
                     \[\frac{q}{4{{\varepsilon }_{0}}}\]                           done clear
  D)
             \[\frac{q}{6{{\varepsilon }_{0}}}\] done clear
  View Solution play_arrow

• question_answer8)
  Two infinitely long parallel wires having linear charge densities \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] respectively are placed at a distance of R metres. The force per unit length on either wire will be \[\left( K=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)\]   [MP PMT/PET 1998; DPMT 2000]
  A)
                     \[K\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{2}}}\] done clear
  B)
                                       \[K\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{R}\] done clear
  C)
                     \[K\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{2}}}\]               done clear
  D)
             \[K\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{R}\] done clear
  View Solution play_arrow

• question_answer9)
  Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If Q1 coulomb and Q2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge qfrom the centre of one ring to that of other is                                                            [MP PMT 1999; AMU (Engg.) 1999]
  A)
                     Zero done clear
  B)
                                       \[\frac{q({{Q}_{1}}-{{Q}_{2}})(\sqrt{2}-1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] done clear
  C)
                     \[\frac{q\sqrt{2}({{Q}_{1}}+{{Q}_{2}})}{4\pi {{\varepsilon }_{0}}R}\]      done clear
  D)
             \[\frac{q({{Q}_{1}}+{{Q}_{2}})(\sqrt{2}+1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] done clear
  View Solution play_arrow

• question_answer10)
  An ellipsoidal cavity is carved within a perfect conductor. A positive charge \[q\] is placed at the centre of the cavity. The points \[A\] and \[B\] are on the cavity surface as shown in the figure. Then                               [IIT-JEE (Screening) 1999]
  A)
             Electric field near \[A\] in the cavity = Electric field near  \[B\] in the cavity done clear
  B)
             Charge density at \[A=\] Charge density at \[B\] done clear
  C)
             Potential at \[A=\] Potential at \[B\] done clear
  D)
             Total electric field flux through the surface of the cavity is \[q/{{\varepsilon }_{0}}\] done clear
  View Solution play_arrow

• question_answer11)
  A charge \[+q\] is fixed at each of the points \[x={{x}_{0}},\,x=3{{x}_{0}},\,x=5{{x}_{0}}\]..... infinite, on the \[x-\]axis and a charge \[-q\]  is fixed at each of the points \[x=2{{x}_{0}},\,x=4{{x}_{0}},x=6{{x}_{0}}\],..... infinite. Here \[{{x}_{0}}\] is a positive constant. Take the electric potential at a point due to a charge \[Q\] at a distance \[r\] from it to be \[Q/(4\pi {{\varepsilon }_{0}}r)\]. Then, the potential at the origin due to the above system of charges is                                                                         [IIT 1998]
  A)
                     0                                         done clear
  B)
             \[\frac{q}{8\pi {{\varepsilon }_{0}}{{x}_{0}}\ln 2}\] done clear
  C)
                     \[\infty \]                        done clear
  D)
             \[\frac{q\ln 2}{4\pi {{\varepsilon }_{0}}{{x}_{0}}}\] done clear
  View Solution play_arrow

• question_answer12)
  A positively charged thin metal ring of radius \[R\] is fixed in the \[xy-\]plane with its centre at the \[O\]. A negatively charged particle \[P\] is released from rest at the point  \[(0,\,0,\,{{z}_{0}})\], where \[{{z}_{0}}>0\]. Then the motion of \[P\] is                                                                                                    [IIT 1998]
  A)
                     Periodic for all values of \[{{z}_{0}}\] satisfying \[0<{{z}_{0}}<\infty \] done clear
  B)
                     Simple harmonic for all values of satisfying \[0<{{z}_{0}}<R\] done clear
  C)
                     Approximately simple harmonic provided \[{{z}_{0}}<<R\] done clear
  D)
                     Such that \[P\] crosses \[O\] and continues to move along the negative \[z-\]axis towards \[z=-\infty \] done clear
  View Solution play_arrow

• question_answer13)
  A non-conducting solid sphere of radius \[R\] is uniformly charged. The magnitude of the electric field due to the sphere at a distance \[r\] from its centre                                                                          [IIT-JEE 1998; DPMT 2000]
  A)
                     Increases as \[r\] increases for \[r<R\] done clear
  B)
                     Decreases as \[r\] increases for \[0<r<\infty \] done clear
  C)
                     Decreases as \[r\] increases for \[R<r<\infty \] done clear
  D)
                     Is discontinuous at \[r=R\] done clear
  View Solution play_arrow

• question_answer14)
  A non-conducting ring of radius \[0.5\,m\] carries a total charge of \[1.11\times {{10}^{-10}}C\] distributed non-uniformly on its circumference producing an electric field \[\vec{E}\] everywhere in space. The value of the line integral \[\int_{l=\infty }^{l=0}{\,-\overrightarrow{E}.\overrightarrow{dl}}\,(l=0\] being centre of the ring) in volt is                                                                       [IIT 1997 Cancelled]
  A)
                     + 2 done clear
  B)
             ? 1 done clear
  C)
                     ? 2                                     done clear
  D)
             Zero done clear
  View Solution play_arrow

• question_answer15)
  A negatively charged plate has charge density of \[2\times {{10}^{-6}}C/{{m}^{2}}\]. The initial distance of an electron which is moving toward plate, cannot strike the plate, if it is having energy of \[200\,eV\]                                             [RPET 1997]
  A)
                     \[1.77\,mm\] done clear
  B)
                                       \[3.51\,mm\] done clear
  C)
                     \[1.77\,cm\] done clear
  D)
                                       \[3.51\,cm\] done clear
  View Solution play_arrow

• question_answer16)
  The charge on \[500\,cc\] of water due to protons will be [RPET 1997]
  A)
                     \[6.0\times {{10}^{27}}C\] done clear
  B)
                                       \[2.67\times {{10}^{7}}C\] done clear
  C)
                     \[6\times {{10}^{23}}C\]  done clear
  D)
             \[1.67\times {{10}^{23}}C\] done clear
  View Solution play_arrow

• question_answer17)
  Electric potential is given by \[V=6x-8x{{y}^{2}}-8y+6yz-4{{z}^{2}}\]            Then electric force acting on \[2C\] point charge placed on origin will be                                     [RPET 1999]
  A)
                     \[2N\] done clear
  B)
                                       \[6N\] done clear
  C)
                     \[8N\]                              done clear
  D)
             \[20\,N\] done clear
  View Solution play_arrow

• question_answer18)
  The electric field in a region is radially outward with magnitude \[E=A{{\gamma }_{0}}\]. The charge contained in a sphere of radius \[{{\gamma }_{0}}\] centered at the origin is     [AMU 1999]
  A)
             \[\frac{1}{4\pi {{\varepsilon }_{0}}}A\gamma _{0}^{3}\]     done clear
  B)
             \[4\pi {{\varepsilon }_{0}}A\gamma _{0}^{3}\] done clear
  C)
             \[\frac{4\pi {{\varepsilon }_{0}}A}{{{\gamma }_{0}}}\]         done clear
  D)
             \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{\gamma _{0}^{3}}\] done clear
  View Solution play_arrow

• question_answer19)
  Charge \[q\] is uniformly distributed over a thin half ring of radius \[R\]. The electric field at the centre of the ring is                                                                                          [Roorkee 1999]
  A)
             \[\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{R}^{2}}}\] done clear
  B)
                                       \[\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{R}^{2}}}\] done clear
  C)
             \[\frac{q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]           done clear
  D)
             \[\frac{q}{2\pi {{\varepsilon }_{0}}{{R}^{2}}}\] done clear
  View Solution play_arrow

• question_answer20)
  In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that q is so small that \[\tan \theta \approx \sin \theta \], then for equilibrium x is equal to                                              [AMU 2000]
  A)
             \[{{\left( \frac{{{q}^{2}}L}{2\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\] done clear
  B)
                                       \[{{\left( \frac{q{{L}^{2}}}{2\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\] done clear
  C)
             \[{{\left( \frac{{{q}^{2}}{{L}^{2}}}{4\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]         done clear
  D)
             \[{{\left( \frac{{{q}^{2}}L}{4\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\] done clear
  View Solution play_arrow

• question_answer21)
  Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible [AMU 2001]
  A)
             \[|{{\overrightarrow{E}}_{1}}|\,=\,|{{\overrightarrow{E}}_{2}}|,\ {{V}_{1}}={{V}_{2}}\] done clear
  B)
                                       \[{{\overrightarrow{E}}_{1}}\ne {{\overrightarrow{E}}_{2}},\ {{V}_{1}}\ne {{V}_{2}}\] done clear
  C)
             \[{{\overrightarrow{E}}_{1}}\ne {{\overrightarrow{E}}_{2}},\ {{V}_{1}}={{V}_{2}}\]               done clear
  D)
             \[|{{\overrightarrow{E}}_{1}}|\,=\,|{{\overrightarrow{E}}_{2}}|,\ {{V}_{1}}\ne {{V}_{2}}\] done clear
  View Solution play_arrow

• question_answer22)
  Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in                         [IIT-JEE (Screening) 2001]           
  A)
                                     done clear
  B)
             done clear
  C)
                                   done clear
  D)
             done clear
  View Solution play_arrow

• question_answer23)
  A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at \[x=+1\]cm and C be the point on the y-axis at \[y=+1\]cm. Then the potentials at the points A, B and C satisfy                                                               [IIT-JEE (Screening) 2001]
  A)
             \[{{V}_{A}}<{{V}_{B}}\] done clear
  B)
                                       \[{{V}_{A}}>{{V}_{B}}\] done clear
  C)
             \[{{V}_{A}}<{{V}_{C}}\]    done clear
  D)
             \[{{V}_{A}}>{{V}_{C}}\] done clear
  View Solution play_arrow

• question_answer24)
  There is a uniform electric field of strength \[{{10}^{3}}\,V/m\] along y-axis. A body of mass 1g and charge \[\text{1}{{0}^{\text{6}}}C\] is projected into the field from origin along the positive x-axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation) [EAMCET 2001]
  A)
             10   done clear
  B)
             \[5\sqrt{2}\] done clear
  C)
             \[10\sqrt{2}\]                       done clear
  D)
             20 done clear
  View Solution play_arrow

• question_answer25)
  The electric potential at a point \[(x,\ y)\] in the \[x-y\] plane is given by \[V=-kxy\]. The field intensity at a distance \[r\] from the origin varies as                                [UPSEAT 2002]
  A)
             \[{{r}^{2}}\]                           done clear
  B)
             r done clear
  C)
             \[\frac{1}{r}\]                       done clear
  D)
             \[\frac{1}{{{r}^{2}}}\] done clear
  View Solution play_arrow

• question_answer26)
  Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when   [MP PET 2002]
  A)
             \[x=\frac{d}{\sqrt{2}}\] done clear
  B)
                                       \[x=\frac{d}{2}\] done clear
  C)
             \[x=\frac{d}{2\sqrt{2}}\]  done clear
  D)
             \[x=\frac{d}{2\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer27)
  Two equal point charges are fixed at \[x=-a\] and \[x=+a\] on the x-axis. Another point charge Q is placed at the origin. The Change in the electrical potential energy of Q, when it is displaced by a small distance \[x\] along the x-axis, is approximately proportional to [IIT-JEE (Screening) 2002]
  A)
             x     done clear
  B)
             \[{{x}^{2}}\] done clear
  C)
             \[{{x}^{3}}\]                          done clear
  D)
             \[1/x\] done clear
  View Solution play_arrow

• question_answer28)
  An elementary particle of mass \[m\] and charge \[+e\] is projected with velocity \[v\] at a much more massive particle of charge \[Ze,\] where \[Z>0.\]What is the closest possible approach of the incident particle                     [Orissa JEE 2002]
  A)
             \[\frac{Z{{e}^{2}}}{2\pi {{\varepsilon }_{0}}m{{v}^{2}}}\] done clear
  B)
                                       \[\frac{Ze}{4\pi {{\varepsilon }_{0}}m{{v}^{2}}}\] done clear
  C)
             \[\frac{Z{{e}^{2}}}{8\pi {{\varepsilon }_{0}}m{{v}^{2}}}\]    done clear
  D)
             \[\frac{Ze}{8\pi {{\varepsilon }_{0}}m{{v}^{2}}}\] done clear
  View Solution play_arrow

• question_answer29)
  An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is [MP PET 2003]
  A)
             \[{{\left( \frac{pE}{I} \right)}^{1/2}}\] done clear
  B)
                                       \[{{\left( \frac{pE}{I} \right)}^{3/2}}\] done clear
  C)
             \[{{\left( \frac{I}{pE} \right)}^{1/2}}\]                            done clear
  D)
             \[{{\left( \frac{p}{IE} \right)}^{1/2}}\] done clear
  View Solution play_arrow

• question_answer30)
  A metallic shell has a point charge ?q? kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces                       [IIT-JEE (Screening) 2003]
  A)
                                  done clear
  B)
  done clear
  C)
    done clear
  D)
                                    done clear
  View Solution play_arrow

• question_answer31)
  An infinite number of electric charges each equal to 5 nano-coulomb (magnitude) are placed along X-axis at \[x=1\]cm, \[x=2\]cm, \[x=4\]cm \[x=8\]cm ???. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at \[x=0\] is  \[\left( \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N-{{m}^{2}}/{{c}^{2}} \right)\]                                  [EAMCET 2003]
  A)
             \[12\times {{10}^{4}}\] done clear
  B)
                                       \[24\times {{10}^{4}}\] done clear
  C)
             \[36\times {{10}^{4}}\]     done clear
  D)
             \[48\times {{10}^{4}}\] done clear
  View Solution play_arrow

• question_answer32)
  A small sphere carrying a charge ?q? is hanging in between two parallel plates by a string of length L. Time period of pendulum is \[{{T}_{0}}\]. When parallel plates are charged, the time period changes to \[T\]. The ratio \[T/{{T}_{0}}\] is equal to [UPSEAT 2003]
  A)
             \[{{\left( \frac{g+\frac{qE}{m}}{g} \right)}^{1/2}}\] done clear
  B)
                                       \[{{\left( \frac{g}{g+\frac{qE}{m}} \right)}^{3/2}}\] done clear
  C)
             \[{{\left( \frac{g}{g+\frac{qE}{m}} \right)}^{1/2}}\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer33)
  Three charges \[-{{q}_{1}},\,\,+{{q}_{2}}\] and \[-{{q}_{3}}\] are placed as shown in the figure. The x-component of the force on \[-{{q}_{1}}\] is proportional to                                                        [AIEEE 2003]
  A)
             \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \] done clear
  B)
             \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \] done clear
  C)
             \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \] done clear
  D)
             \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \] done clear
  View Solution play_arrow

• question_answer34)
  A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V.  If the shell is now given a charge of ?3Q, the new potential difference between the same two surfaces is [IIT 1989]
  A)
             V     done clear
  B)
             2V done clear
  C)
             4V  done clear
  D)
             ? 2V done clear
  View Solution play_arrow

• question_answer35)
  Two point charges \[+q\] and \[-q\] are held fixed at \[(-d,\,0)\] and \[(d,\,0)\] respectively of a \[(X,\,Y)\] coordinate system. Then  [IIT 1995]
  A)
                     E at all points on the \[Y-\]axis is along \[\hat{i}\] done clear
  B)
                     The electric field \[\overrightarrow{E}\] at all points on the \[X-\]axis has the same direction done clear
  C)
                     Dipole moment is \[2qd\] directed along \[\hat{i}\] done clear
  D)
                     Work has to be done in bringing a test charge from infinity to the origin done clear
  View Solution play_arrow

• question_answer36)
  A point charge of 40 stat coulomb is placed 2 cm in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is
  A)
             100 dynes done clear
  B)
             160 dynes done clear
  C)
             1600 dynes                             done clear
  D)
             400 dynes done clear
  View Solution play_arrow

• question_answer37)
  A piece of cloud having area \[25\times {{10}^{6}}{{m}^{2}}\] and electric potential of \[{{10}^{5}}\] volts. If the height of cloud is \[0.75\,km\], then energy of electric field between earth and cloud will be [RPET 1997]
  A)
                                                       \[250\,J\]                                done clear
  B)
             \[750\,J\] done clear
  C)
                     \[1225J\] done clear
  D)
                                       \[1475J\] done clear
  View Solution play_arrow

• question_answer38)
  Two point charges \[(+Q)\] and \[(-2Q)\] are fixed on the X-axis at positions \[a\] and \[2a\] from origin respectively. At what positions on the axis, the resultant electric field is zero                    [MP PET 2001]
  A)
             Only \[x=\sqrt{2}a\]          done clear
  B)
             Only \[x=-\sqrt{2}a\] done clear
  C)
             Both \[x=\pm \sqrt{2}a\] done clear
  D)
             \[x=\frac{3a}{2}\] only done clear
  View Solution play_arrow

• question_answer39)
  Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q, R, S, T and U respectively [IIT-JEE (Screening) 2004]
  A)
                                                       \[+,\,-,\,+,\,-,\,-,\,+\] done clear
  B)
                     \[+,\,-,\,+,\,-,\,+,\,-\] done clear
  C)
                     \[+,\,+,\,-,\,+,\,-,\,-\] done clear
  D)
                     \[-,\,+,\,+,\,-,\,+,\,-\] done clear
  View Solution play_arrow

• question_answer40)
  A charged particle q is shot towards another charged particle Q which is fixed, with a speed \[\nu \]. It approaches Q upto a closest distance r and then returns. If q were given a speed \[2\nu \], the closest distances of approach would be                                                                                                            [AIEEE 2004]
  A)
                     r done clear
  B)
                                       2r done clear
  C)
                     r/2                                     done clear
  D)
             r/4 done clear
  View Solution play_arrow

• question_answer41)
  Four charges equal to ? Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is                                      [AIEEE 2004]
  A)
                     \[-\frac{Q}{4}(1+2\sqrt{2})\] done clear
  B)
                                       \[\frac{Q}{4}(1+2\sqrt{2})\] done clear
  C)
                     \[-\frac{Q}{2}(1+2\sqrt{2})\]                                      done clear
  D)
             \[\frac{Q}{2}(1+2\sqrt{2})\] done clear
  View Solution play_arrow

• question_answer42)
  A parallel plate air capacitor has a capacitance of \[100\mu \mu F\].  The plates are at a distance \[d\]apart. If a slab of thickness   \[t(t\le d)\]and dielectric constant 5 is introduced between the parallel plates, then the capacitance will be                    [MP PMT 2003]
  A)
                     \[50\mu \mu F\] done clear
  B)
                                       \[100\mu \mu F\] done clear
  C)
                     \[200\mu \mu F\] done clear
  D)
             \[500\mu \mu F\] done clear
  View Solution play_arrow

• question_answer43)
  A dielectric slab of thickness \[d\] is inserted in a parallel plate capacitor whose negative plate is at \[x=0\] and positive plate is at \[x=3d\]. The slab is equidistant from the plates. The capacitor is given some charge. As one goes from 0 to \[3d\] [IIT-JEE 1998]
  A)
                     The magnitude of the electric field remains the same done clear
  B)
                     The direction of the electric field remains the same done clear
  C)
                     The electric potential increases continuously done clear
  D)
                     The electric potential increases at first, then decreases and again increases done clear
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• question_answer44)
  nnCapacitance of a capacitor made by a thin metal foil is \[2\mu F\]. If the foil is folded with paper of thickness\[0.15mm\], dielectric constant of paper is 2.5 and width of paper is\[400mm\], then length of foil will be                   [RPET 1997]
  A)
                     \[0.34\ m\] done clear
  B)
                                       \[1.33\ m\] done clear
  C)
                     \[13.4\ m\]                     done clear
  D)
             \[33.9\ m\] done clear
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• question_answer45)
  A parallel plate capacitor is charged to a potential difference of 50 V. It is discharged through a resistance. After 1 second, the potential difference between plates becomes 40 V. Then [Roorkee 1999]
  A)
             Fraction of stored energy after 1 second is 16/25 done clear
  B)
             Potential difference between the plates after 2 seconds will be 32 V done clear
  C)
             Potential difference between the plates after 2 seconds will be 20 V done clear
  D)
             Fraction of stored energy after 1 second is 4/5 done clear
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• question_answer46)
  A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If x is the separation between the plates, the time rate of change of electrostatic energy of capacitor is proportional to                                                                                              [CPMT 2002]
  A)
             \[{{x}^{\text{2}}}\]             done clear
  B)
             x done clear
  C)
             \[{{x}^{\text{1}}}\]             done clear
  D)
             \[{{x}^{\text{2}}}\] done clear
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• question_answer47)
  Five identical plates each of area A are joined as shown in the figure. The distance between the plates is d. The plates are connected to a potential difference of \[V\ volts\]. The charge on plates 1 and 4 will be                         [IIT 1984]
  A)
                     \[\frac{{{\varepsilon }_{0}}AV}{d}.\frac{2{{\varepsilon }_{0}}AV}{d}\] done clear
  B)
                     \[\frac{{{\varepsilon }_{0}}AV}{d}.\frac{2{{\varepsilon }_{0}}AV}{d}\]  done clear
  C)
                     \[\,\frac{{{\varepsilon }_{0}}AV}{d}.\frac{-2{{\varepsilon }_{0}}AV}{d}\] done clear
  D)
                     \[\frac{-{{\varepsilon }_{0}}AV}{d}.\frac{-2{{\varepsilon }_{0}}AV}{d}\] done clear
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• question_answer48)
  To form a composite \[16\mu F,\ 1000V\] capacitor from a supply of identical capacitors marked \[8\mu F,\ 250V\], we require a minimum number of capacitors                                                                       [MP PET 1996; AIIMS 2000]
  A)
                     40                                       done clear
  B)
             32 done clear
  C)
                     8                                         done clear
  D)
             2 done clear
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• question_answer49)
  An infinite number of identical capacitors each of capacitance \[1\mu F\] are connected as in adjoining figure. Then the equivalent capacitance between \[A\] and \[B\] is                                                                                           [EAMCET 1990]
  A)
                     \[1\mu F\] done clear
  B)
                     \[2\mu F\] done clear
  C)
                     \[\frac{1}{2}\mu F\] done clear
  D)
                     \[\infty \] done clear
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• question_answer50)
  Two condensers of capacities \[2C\] and C are joined in parallel and charged upto potential V. The battery is removed and the condenser of capacity C is filled completely with a medium of dielectric constant K. The p.d. across the capacitors will now be                          [IIT 1988]
  A)
                     \[\frac{3V}{K+2}\] done clear
  B)
                                       \[\frac{3V}{K}\] done clear
  C)
                     \[\frac{V}{K+2}\]         done clear
  D)
             \[\frac{V}{K}\] done clear
  View Solution play_arrow

• question_answer51)
  In the figure below, what is the potential difference between the point A and B and between B and C respectively in steady state                                                                          [IIT 1979]
  A)
                                                       \[{{V}_{AB}}={{V}_{BC}}=100\,V\] done clear
  B)
                                       \[{{V}_{AB}}=75\,V,\ {{V}_{BC}}=25\ V\] done clear
  C)
                     \[{{V}_{AB}}=25\,V,\ {{V}_{BC}}=75\ V\] done clear
  D)
             \[{{V}_{AB}}={{V}_{BC}}=50\ V\] done clear
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• question_answer52)
  Figure given below shows two identical parallel plate capacitors connected to a battery with switch \[S\]closed. The switch is now opened and the free space between the plate of capacitors is filled with a dielectric of dielectric constant 3. What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric                                                    [IIT 1983]
  A)
                     3 : 1 done clear
  B)
                     5 : 1 done clear
  C)
                     3 : 5 done clear
  D)
                     5 : 3 done clear
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• question_answer53)
  A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is connected to another battery and is charged to potential difference 2V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is [IIT 1995]
  A)
                     Zero done clear
  B)
                                       \[\frac{25C{{V}^{2}}}{6}\] done clear
  C)
                     \[\frac{3C{{V}^{2}}}{2}\]  done clear
  D)
             \[\frac{9C{{V}^{2}}}{2}\] done clear
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• question_answer54)
  Condenser \[A\] has a capacity of \[15\mu F\] when it is filled with a medium of dielectric constant 15. Another condenser \[B\] has a capacity of \[1\mu F\]with air between the plates. Both are charged separately by a battery of\[100\ V\]. After charging, both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is                                                               [MNR 1994]
  A)
                     \[400V\] done clear
  B)
                                       \[800\ V\]                               done clear
  C)
                     \[1200\ V\]                     done clear
  D)
             \[1600\ V\] done clear
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• question_answer55)
  Four metallic plates each with a surface area of one side A are placed at a distance d from each other. The plates are connected as shown in the circuit diagram. Then the capacitance of the system between \[a\] and \[b\] is
  A)
                     \[\frac{3{{\varepsilon }_{0}}A}{d}\] done clear
  B)
                     \[\frac{2{{\varepsilon }_{0}}A}{d}\] done clear
  C)
                     \[\frac{2{{\varepsilon }_{0}}A}{3d}\] done clear
  D)
                     \[\frac{3{{\varepsilon }_{0}}A}{2d}\] done clear
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• question_answer56)
  In the given circuit if point C is connected to the earth and a potential of \[+\,2000\,V\] is given to the point A, the potential at B is                                     [MP PET 1997; Pb. PET 2003]
  A)
             \[1500\,V\] done clear
  B)
                     \[1000\ V\] done clear
  C)
                     \[500\ V\] done clear
  D)
                     \[400\ V\] done clear
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• question_answer57)
  A finite ladder is constructed by connecting several sections of \[2\mu F,\ 4\mu F\] capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between [MP PMT 1999; KCET (Engg./Med.) 1999]
  A)
                                                       \[4\mu F\] done clear
  B)
                     \[2\mu F\] done clear
  C)
                     \[18\mu F\] done clear
  D)
                     \[6\mu F\] done clear
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• question_answer58)
  In an isolated parallel plate capacitor of capacitance C, the four surface have charges \[{{Q}_{1}}\], \[{{Q}_{2}}\], \[{{Q}_{3}}\] and \[{{Q}_{4}}\] as shown. The potential difference between the plates is [IIT-JEE 1999]
  A)
             \[\frac{{{Q}_{1}}+{{Q}_{2}}+{{Q}_{3}}+{{Q}_{4}}}{2C}\] done clear
  B)
    \[\frac{{{Q}_{2}}+{{Q}_{3}}}{2C}\] done clear
  C)
   \[\frac{{{Q}_{2}}-{{Q}_{3}}}{2C}\] done clear
  D)
             \[\frac{{{Q}_{1}}+{{Q}_{4}}}{2C}\] done clear
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• question_answer59)
  For the circuit shown, which of the following statements is true                [IIT-JEE 1999; UPSEAT 2003]
  A)
                                                      With \[{{S}_{1}}\]closed, \[{{V}_{1}}=15\,V,\ {{V}_{2}}=20\ V\] done clear
  B)
                     With \[{{S}_{3}}\] closed \[{{V}_{1}}={{V}_{2}}=25V\] done clear
  C)
                     With \[{{S}_{1}}\] and \[{{S}_{2}}\] closed \[{{V}_{1}}={{V}_{2}}=0\]  done clear
  D)
                     With\[{{S}_{1}}\]and \[{{S}_{3}}\]closed, \[{{V}_{1}}=30\,V,\ {{V}_{2}}=20\,V\] done clear
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• question_answer60)
  Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is                        [IIT-JEE (Screening) 2001]
  A)
             Zero done clear
  B)
                                       \[q/2\] done clear
  C)
             q     done clear
  D)
             \[2q\] done clear
  View Solution play_arrow

• question_answer61)
  A capacitor of capacitance \[{{C}_{\text{1}}}=\text{ 1}\mu F\] can with stand maximum voltage \[{{V}_{\text{1}}}=\text{ 6}kV\left( kilo-volt \right)\] and another capacitor of capacitance \[{{C}_{\text{2}}}=\text{3}\mu F\] can withstand maximum voltage \[{{V}_{\text{2}}}=\text{ 4}kV\]. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of                                  [MP PET 2001]
  A)
             \[4\,kV\]                                 done clear
  B)
             \[6\,kV\] done clear
  C)
             \[8\,kV\]                                 done clear
  D)
             \[10\,kV\] done clear
  View Solution play_arrow

• question_answer62)
  In the given figure each plate of capacitance C has partial value of charge                                              [MP PMT 2003]
  A)
             CE done clear
  B)
             \[\frac{CE{{R}_{1}}}{{{R}_{2}}-r}\] done clear
  C)
             \[\frac{CE{{R}_{2}}}{{{R}_{2}}+r}\] done clear
  D)
             \[\frac{CE{{R}_{1}}}{{{R}_{1}}-r}\] done clear
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• question_answer63)
  The plates of a capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After 1 second  the potential difference between the plates of the capacitor is 240 volts, then after 2 and 3 seconds the potential difference between the plates will be                                                               [MP PET 1996]
  A)
             200 and 180 V done clear
  B)
                                       180 and 135 V done clear
  C)
             160 and 80 V                          done clear
  D)
             140 and 20 V done clear
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• question_answer64)
  The plates of a parallel plate condenser are pulled apart with a velocity \[v\]. If at any instant their mutual distance of separation is \[d\], then the magnitude of the time of rate of change of capacity depends on \[d\] as follows                        [MP PET 1991]
  A)
             \[\frac{1}{d}\]                      done clear
  B)
             \[\frac{1}{{{d}^{2}}}\] done clear
  C)
             \[{{d}^{2}}\]                          done clear
  D)
             \[d\] done clear
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• question_answer65)
  A fully charged capacitor has a capacitance ?C?. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ?s? and mass ?m?. If the temperature of the block is raised by ?\[\Delta T\]?, the potential difference ?V? across the capacitance is [AIEEE 2005]
  A)
             \[\frac{ms\Delta T}{C}\]   done clear
  B)
             \[\sqrt{\frac{2ms\Delta T}{C}}\] done clear
  C)
             \[\sqrt{\frac{2mC\Delta T}{s}}\]                                       done clear
  D)
             \[\frac{mC\Delta T}{s}\] done clear
  View Solution play_arrow

• question_answer66)
  A network of four capacitors of capacity equal to \[{{C}_{1}}=C,\,\,{{C}_{2}}=2C,\,{{C}_{3}}=3C\] and \[{{C}_{4}}=4C\] are conducted in a battery as shown in the figure. The ratio of the charges on \[{{C}_{2}}\] and \[{{C}_{4}}\] is                                                                  [CBSE PMT 2005]
  A)
             \[\frac{22}{3}\] done clear
  B)
             \[\frac{3}{22}\] done clear
  C)
             \[\frac{7}{4}\] done clear
  D)
             \[\frac{4}{7}\] done clear
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• question_answer67)
  A 4 mF capacitor, a resistance of 2.5 MW is in series with 12 V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given ln(2)= 0.693] [IIT-JEE (Screening) 2005]
  A)
             13.86 s done clear
  B)
                                       6.93 s done clear
  C)
                  7 s           done clear
  D)
                  14 s done clear
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