JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank

done Mock Test - Electrostatics Total Questions - 25

• question_answer1)
  A soap bubble (surface tension =\[T\]) is charged to a maximum surface density of charge =\[\sigma \]. When it is just going to burst? Its radius R is given by
  A)
  \[R=\frac{{{\sigma }^{2}}}{8{{\varepsilon }_{0}}T}\]   done clear
  B)
  \[R=8{{\varepsilon }_{0}}\frac{T}{{{\sigma }^{2}}}\] done clear
  C)
  \[R=\frac{{{\sigma }^{{}}}}{\sqrt{8{{\varepsilon }_{0}}T}}\]    done clear
  D)
  \[R=\frac{{{\sqrt{8{{\varepsilon }_{0}}T}}^{{}}}}{\sigma }\] done clear
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• question_answer2)
  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 \[\left( k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)\]
  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
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• question_answer3)
  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 \[\theta \] is so small that\[\tan \theta \]\[\approx \]\[\sin \theta \], then for equilibrium \[x\] is equal to
  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
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• question_answer4)
  Two point charges \[100\mu C\]and \[5\mu C\] are placed at points \[A\] and \[B\] respectively with \[AB\] = 40 cm. The work done by external force in displacing the charge 5 \[\mu C\] from \[B\] to \[C\], where \[BC\] = 30 cm, angle \[ABC\] = \[\pi /2\] and \[1/4\pi {{\varepsilon }_{0}}=9\times {{10}^{9}}N{{m}^{2}}/{{C}^{2}}\]
  A)
  \[9J\]     done clear
  B)
  \[\frac{81}{20}J\] done clear
  C)
  \[\frac{9}{25}J\]            done clear
  D)
  \[-\frac{9}{4}J\] done clear
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• question_answer5)
  Two identical thin rings each of radius \[R\] meters are coaxially placed at a distance R meters apart. If \[{{Q}_{1}}\] coulomb and \[{{Q}_{2}}\] coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge\[q\] from the centre of one ring to that of other is
  A)
  Zero                  done clear
  B)
  \[\frac{q({{Q}_{2}}-{{Q}_{1}})(\sqrt{2}-1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] 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
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• question_answer6)
  Two semicircular rings lying in the same plane of uniform linear charge density \[\lambda \] have radii r and 2r. They are joined using two straight uniformly charged wires of linear charge density \[\lambda \] and length r as shown in the figure. The magnitude of electric field at common centre of semi-circular rings is
  A)
  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3\lambda }{2r}\]                       done clear
  B)
  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\lambda }{2r}\] done clear
  C)
  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2\lambda }{r}\] done clear
  D)
  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\lambda }{r}\] done clear
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• question_answer7)
  A uniformly charged and infinitely long line having a liner charge density \[\lambda \] is placed at a normal distance \[y\] from a point O. Consider a sphere of radius \[R\] with O as the center and \[R\] > \[y\]. Electric flux through the surface of the sphere is
  A)
  Zero                  done clear
  B)
  \[\frac{2\lambda R}{{{\varepsilon }_{0}}}\] done clear
  C)
  \[\frac{2\lambda \sqrt{{{R}^{2}}-{{y}^{2}}}}{{{\varepsilon }_{0}}}\] done clear
  D)
  \[\frac{\lambda \sqrt{{{R}^{2}}+{{y}^{2}}}}{{{\varepsilon }_{0}}}\] done clear
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• question_answer8)
  A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring is q, and the linear charge density on the straight wire is\[\lambda \]. The interaction force between the ring and the wire is
  A)
  \[\frac{\lambda q}{4\pi {{\varepsilon }_{0}}r}\]   done clear
  B)
  \[\frac{\lambda q}{2\sqrt{2}\pi {{\varepsilon }_{0}}r}\] done clear
  C)
  \[\frac{2\sqrt{2}\lambda q}{\pi {{\varepsilon }_{0}}r}\]    done clear
  D)
  \[\frac{4\lambda q}{\pi {{\varepsilon }_{0}}r}\] done clear
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• question_answer9)
  A positively charged particle moving along \[x\]-axis with a certain velocity enters a uniform electric field directed along positives\[y\]-axis. Its
  A)
  Vertical velocity changes but horizontal velocity remains constant done clear
  B)
  Horizontal velocity changes but vertical velocity remains constant done clear
  C)
  Both vertical and horizontal velocities change done clear
  D)
  Neither vertical nor horizontal velocity changes done clear
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• question_answer10)
  An uncharged aluminum block has a cavity within it. The block is placed in a region where a uniform electric field is directed upward. Which of the following is a correct statement describing conditions in the interior of the block's cavity?
  A)
  The electric field in the cavity is directed upward. done clear
  B)
  The electric field in the cavity is directed downward. done clear
  C)
  There is no electric field in the cavity. done clear
  D)
  The electric field in the cavity is of varying magnitude and is zero at the exact center. done clear
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• question_answer11)
  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
  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
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• question_answer12)
  A small conducting sphere of radius\[a\], carrying a charge\[+Q\], is placed inside an equal and oppositely charged conducting shell of radius b such that their centers coincide. Determine the potential at a point which is at a distance c from center such that a < c < b.
  A)
  \[k(Q/c+Q/b)\] done clear
  B)
  \[k(Q/a+Q/b)\] done clear
  C)
  \[k(Q/a-Q/b)\] done clear
  D)
  \[k(Q/c-Q/b)\] done clear
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• question_answer13)
  At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along
  A)
  North    done clear
  B)
  South done clear
  C)
  North-south        done clear
  D)
  East-west done clear
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• question_answer14)
  Variation of electrostatic potential along the \[x\]-direction is shown in figure. The correct statement about electric field is
  A)
  \[x\]-component at point B is maximum done clear
  B)
  \[x\]-component at point A is toward positive \[x\]-axis done clear
  C)
  \[x\]-component at point C is along negative \[x\]-axis done clear
  D)
  \[x\]-component at point C is along positive \[x\]- axis done clear
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• question_answer15)
  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
  A)
  \[{{\left( \frac{pE}{l} \right)}^{1/2}}\]    done clear
  B)
  \[{{\left( \frac{pE}{l} \right)}^{3/2}}\] done clear
  C)
  \[{{\left( \frac{l}{pE} \right)}^{1/2}}\]                done clear
  D)
  \[{{\left( \frac{p}{lE} \right)}^{1/2}}\] done clear
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• question_answer16)
  The potential field depends on the \[x\]- and \[y\]coordinates as \[V={{x}^{2}}-{{y}^{2}}\]. The corresponding electric field lines in \[xy\] plane are as
  A)
            done clear
  B)
  done clear
  C)
               done clear
  D)
  done clear
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• question_answer17)
  A charged oil drop is suspended in a uniform field of \[3\times {{10}^{4}}V/m\] so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge as \[9.9\times {{10}^{-15}}kg\,and\,g\,as\,10m/{{s}^{2}}\]
  A)
  \[3.3\times {{10}^{-18}}C\]      done clear
  B)
  \[3.2\times {{10}^{-18}}C\] done clear
  C)
  \[1.6\times {{10}^{-18}}C\]      done clear
  D)
  \[4.8\times {{10}^{-18}}C\] done clear
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• question_answer18)
  It is required to hold equal charges \[q\] in equilibrium at the comers of a square. What charge when placed at the center of the square will do this?
  A)
  \[-\frac{q}{2}(1+2\sqrt{2})\]       done clear
  B)
  \[\frac{q}{2}(1+2\sqrt{2})\] done clear
  C)
  \[\frac{q}{4}(1+2\sqrt{2})\]        done clear
  D)
  \[-\frac{q}{4}(1+2\sqrt{2})\] done clear
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• question_answer19)
  The electric flux from a cube of edge \[l\] is\[\phi \]. If an edge of the cube is made \[2l\] and the charge enclosed is halved, its value will be
  A)
  \[4\phi \]                        done clear
  B)
  \[2\phi \] done clear
  C)
  \[\phi /2\]                       done clear
  D)
  \[\phi \] done clear
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• question_answer20)
  The maximum electric field at a point on the axis of a uniformly charged ring is \[{{E}_{0}}\]. At how any points on the axis will the magnitude of the electric field be\[{{E}_{0}}/2\].
  A)
  1                      done clear
  B)
  2 done clear
  C)
  3                      done clear
  D)
  4 done clear
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• question_answer21)
   A linear charge having linear charge density \[\lambda \] penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. What will be the ratio of flux coming cut of cube and sphere?
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• question_answer22)
  There is a uniform electric field of strength \[{{10}^{3}}V/m\] along \[y\]-axis. A body of mass I g and charge \[{{10}^{-6}}C\] is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10 s is (Neglect gravitation)
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• question_answer23)
  Electric potential is given by  \[V=6x-8x{{y}^{2}}-8y+6yz-4{{z}^{2}}\] Then electric force (in N) acting on 2C point charge placed on origin will be _____.
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• question_answer24)
  A flat, square surface with sides of length \[L\] is described by the equations \[x=L,0\le y\le L,0\le z\le L\] The electric flux through the square due to a positive point charge q located at the origin (\[x\] = 0, \[y\] = 0, \[z\] = 0) is \[\frac{q}{N{{\varepsilon }_{0}}}\] Find the value of\[N\]?
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• question_answer25)
  An electric charge \[{{10}^{-3}}\,\mu C\] is placed at the origin (0, 0) of \[x-y\] coordinate system. Two points A and B are situated at \[(\sqrt{2},\sqrt{2})\] and (2, 0), respectively. The potential difference (in V) between the points A and B will be ______.
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