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question_answer1)
Directions: (1-5) |
Electrostatic Potential and Potential Energy |
Electrostatic potential energy of a system of point charges is defined as the total amount of work done in bringing the different charges to their respective positions from infinitely charge mutual separations. The work is stored in the system of two point charges in the form of electrostatic potential energy U of the system. Electric potential difference between any points A and B in an electric field is the amount of work done in moving a unit positive test charge from A to B along any path against the electrostatic force \[{{V}_{B}}-{{V}_{A}}=\frac{{{W}_{AB}}}{{{q}_{0}}}=\int{\overrightarrow{E}}\,.\,dl\]. |
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A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will
A)
remain the same done
clear
B)
increase done
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C)
decrease done
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D)
become zero done
clear
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question_answer2)
Which of the following statement is not true?
A)
Electrostatic force is a conservative force. done
clear
B)
Potential energy of charge q at a point is the work done per unit charge in bringing a charge from any point to infinity. done
clear
C)
Spring force and gravitational force are conservative force. done
clear
D)
Both [a] and [c] done
clear
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question_answer3)
Work done in moving a charge from one point to another inside a uniformly charged conducting sphere is
A)
always zero done
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B)
non-zero done
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C)
may be zero done
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D)
none of these done
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question_answer4)
The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is W. Then the potential \[\phi \] at that point is
A)
\[\frac{WQ}{x}\] done
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B)
W done
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C)
\[\frac{W}{x}\] done
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D)
WQ done
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question_answer5)
If \[1\mu C\]charge is shifted from A to B and it is found that work done by an external force is \[40\,\,\mu J\]. In doing so against electrostatics force, the potential difference \[{{V}_{A}}-{{V}_{B}}\] is
A)
40V done
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B)
- 40V done
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C)
20V done
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D)
- 60V done
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question_answer6)
Directions: (6-10) |
Potential Energy of the Proton |
Potential difference \[\left( \Delta V \right)\]between two points A and B separated by a distance x, in a uniform electric field E is given by \[\Delta V=-Ex\], where x is measured parallel to the field lines. If a charge qo moves from P to Q, the change in potential energy \[\left( \Delta U \right)\]is given as \[\Delta U={{q}_{0}}\Delta V\]. A proton is released from rest in uniform electric field of magnitude \[4\centerdot 0\times {{10}^{8}}V\,{{m}^{-1}}\] directed along the positive X-axis. The proton undergoes a displacement of \[0\centerdot 25m\] in the direction of E. |
Mass of a proton =\[1\centerdot 66\times {{10}^{-27}}\,kg\] and charge of proton \[1\centerdot 6\times {{10}^{-19}}\,C\] |
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The Change in electric potential of the proton between the points A and B is
A)
\[-1\times {{10}^{8}}V\] done
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B)
\[1\times {{10}^{8}}V\] done
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C)
\[6\centerdot 4\times {{10}^{-19}}V\] done
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D)
\[-6\centerdot 4\times {{10}^{-19}}V\] done
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question_answer7)
The Change in electric potential energy of the proton for displacement from A to B is
A)
\[1\centerdot 6\times {{10}^{-11}}J\] done
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B)
\[0\centerdot 5\times {{10}^{-23}}J\] done
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C)
\[-1\centerdot 6\times {{10}^{-11}}J\] done
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D)
\[-3\centerdot 2\times {{10}^{-22}}J\] done
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question_answer8)
The mutual electrostatic potential energy between two protons which are at a distance of \[9\times {{10}^{-15}}m\], in \[_{92}{{U}^{235}}\] nucleus is
A)
\[1\centerdot 56\times {{10}^{-14}}J\] done
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B)
\[5\centerdot 5\times {{10}^{-14}}J\] done
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C)
\[2\centerdot 56\times {{10}^{-14}}J\] done
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D)
\[4\centerdot 56\times {{10}^{-14}}J\] done
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question_answer9)
If a system consists of two charges \[4\,mC\] and \[-3\,mC\] with no external field placed at (-5 cm, 0, 0) and (5 cm, 0, 0) respectively. The amount of work required to separate the two charges infinitely away from each other is
A)
\[-1\centerdot 1\,J\] done
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B)
2J done
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C)
\[2\centerdot 5\,J\] done
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D)
3 J done
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question_answer10)
As the proton moves from P to Q, then
A)
the potential energy of proton decreases done
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B)
the potential energy of proton increases done
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C)
the proton loses kinetic energy done
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D)
total energy of the proton increases. done
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question_answer11)
Directions: (11-15) |
Potential of Two Point Charges |
The potential at any observation point P of a static electric field is defined as the work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge from infinity to the observation point. Figure shows the potential variation along the line of charges. Two point charges \[{{Q}_{1}}\]and \[{{Q}_{2}}\]lie along a line at a distance from each other. |
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At which of the points 1, 2 and 3 is the electric field zero?
A)
1 done
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B)
2 done
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C)
3 done
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D)
Both [a] and [b] done
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question_answer12)
The signs of charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] respectively are
A)
positive and negative done
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B)
negative and positive done
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C)
positive and positive done
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D)
negative and negative done
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question_answer13)
Which of the two charges \[{{Q}_{1}}\]and \[{{Q}_{2}}\] is greater in magnitude ?
A)
\[{{Q}_{2}}\] done
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B)
\[{{Q}_{1}}\] done
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C)
Same done
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D)
Can't determined done
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question_answer14)
Which of the following statement is not true?
A)
Electrostatic force is a conservation force. done
clear
B)
Potential energy of charge q at a point is the work done per unit charge is bringing a charge from any point to infinity. done
clear
C)
When two like charges lie infinite distance apart, their potential energy is zero. done
clear
D)
Both [a] and [c]. done
clear
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question_answer15)
Positive and negative point charges of equal magnitude are kept at \[\left( 0,\,0,\,\frac{a}{2} \right)\] and \[\left( 0,\,0,\,\frac{-a}{2} \right)\]respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is
A)
positive done
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B)
negative done
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C)
zero done
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D)
depends on the path connecting the initial and final positions. done
clear
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question_answer16)
Directions: (16-20) |
Equipotential Surfaces |
For the various charge Systems, we represent equipotential surfaces by curves and line of force by full line curves. Between any two adjacent equipotential surfaces, we assume a constant potential difference the equipotential surfaces of a single point charge are concentric spherical shells with their centres at the point charge. As the lines of force point radially outwards, so they are perpendicular to the equipotential surfaces at all points. |
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Identify the wrong statement.
A)
Equipotential surface due to a single point charge is spherical. done
clear
B)
Equipotential surface can be constructed for dipoles too. done
clear
C)
The electric field is normal to the equipotential surface through the point. done
clear
D)
The work done to move a test charge on the equipotential surface is positive. done
clear
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question_answer17)
Nature of equipotential surface for a point charge is
A)
Ellipsoid with charge at foci done
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B)
Sphere with charge at the centre of the sphere done
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C)
Sphere with charge on the surface of the sphere done
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D)
Plane with charge on the surface. done
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question_answer18)
A spherical equipotential surface is not possible
A)
inside a uniformly charged sphere done
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B)
for a dipole done
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C)
inside a spherical condenser done
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D)
for a point charge done
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question_answer19)
The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is
A)
\[\frac{qQ}{4\pi {{\varepsilon }_{0}}a}\] done
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B)
\[\frac{qQ}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\] done
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C)
\[\frac{q}{4\pi {{\varepsilon }_{0}}a}\] done
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D)
zero done
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question_answer20)
The work done to move a unit charge along an equipotential surface from P to Q
A)
must be defined as \[-\int\limits_{P}^{Q}{\overrightarrow{E}\,}.\,d\overrightarrow{t}\] done
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B)
is zero done
clear
C)
can have a non-zero value done
clear
D)
both [a] and [b] are correct done
clear
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question_answer21)
Directions: (21-25) |
Electric Potential Energy |
This energy possessed by a system of charges by virtue of their positions. When two like charges lie infinite distance apart, their potential energy is zero because no work has to be done in moving one charge at infinite distance from the other. |
In carrying a charge q from point B, work done \[W=q\left( {{V}_{A}}-{{V}_{B}} \right)\] This work may appear as charge in KE/PE of the charge. The potential energy of two charges \[{{q}_{1}}\] and \[{{q}_{2}}\] at a distance r in air is \[\frac{{{q}_{1}}{{q}_{2}}}{4\pi {{\varepsilon }_{0}}r}\]. It is measured in joule. It may be positive, negative or zero depending on the signs of \[{{q}_{1}}\] and \[{{q}_{2}}\]. |
Calculate work done in separating two electrons from a distance of 1 m to 2 m in air, where e is electric charge and k is electrostatic force constant.
A)
\[k{{e}^{2}}\] done
clear
B)
\[{{e}^{2}}/2\] done
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C)
\[-k{{e}^{2}}/2\] done
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D)
zero done
clear
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question_answer22)
Four equal charges q each are placed at four comers of a square of side a each. Work done in carrying a charge -q from its centre to infinity is
A)
zero done
clear
B)
\[\frac{\sqrt{2}q}{\pi {{\varepsilon }_{0}}a}\] done
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C)
\[\frac{\sqrt{2}q}{\pi {{\varepsilon }_{0}}a}\] done
clear
D)
\[\frac{{{q}^{2}}}{\pi {{\varepsilon }_{0}}a}\] done
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question_answer23)
Two points A and B are located in diametrically opposite directions of a point charge of \[+2\,\,\mu C\]at distances 2 m and 1 m respectively from it. The potential difference between A and B is
A)
\[3\times {{10}^{3}}V\] done
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B)
\[6\times {{10}^{4}}V\] done
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C)
\[-9\times {{10}^{3}}V\] done
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D)
\[-3\times {{10}^{3}}V\] done
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question_answer24)
The point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is
A)
\[2\centerdot 0\times {{10}^{-7}}\,J\] done
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B)
\[1\centerdot 35\times {{10}^{-7}}\,J\] done
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C)
\[2\centerdot 7\times {{10}^{-7}}\,J\] done
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D)
\[1\centerdot 21\times {{10}^{-7}}\,J\] done
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question_answer25)
A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V. The work done by an external force in bringing another charge q from infinity up to the point is
A)
\[\frac{V}{q}\] done
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B)
Vq done
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C)
\[V+q\] done
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D)
V done
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question_answer26)
Directions: (26-30) |
Spherical Capacitor |
The electrical capacitance of a conductor is the measure of its ability to hold electric charge. |
An isolated spherical conductor of radius R. The charge Q is uniformly distributed over its entire surface. It can be assumed to be concentrated at the centre of the sphere. |
The potential at any point on the surface of the spherical conductor will be\[V=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{R}\]. |
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Capacitance of the spherical conductor situated in vacuum \[C=\frac{q}{V}=\frac{Q}{\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{R}}\] or \[C=4\pi {{\varepsilon }_{0}}R\] |
Clearly, the capacitance of a spherical conductor is proportional to its radius. |
The radius of the spherical conductor of 1 F capacitance is \[R=\frac{1}{4\pi {{\varepsilon }_{0}}}\]. C and this radius is about 1500 times the radius of the earth\[\left( \tilde{\ }6\times {{10}^{3}}\,km \right)\]. |
If an isolated sphere has a capacitance 50 pF. Then radius is
A)
90 cm done
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B)
45 cm done
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C)
45 m done
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D)
90m done
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question_answer27)
How much charge should be placed on a capacitance of 25 pF to raise its potential to \[{{10}^{5}}V\]?
A)
\[1\mu C\] done
clear
B)
\[1\centerdot 5\mu C\] done
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C)
\[2\,\,\mu C\] done
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D)
\[2\centerdot 5\mu C\] done
clear
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question_answer28)
Dimensions of capacitance is
A)
\[\left[ M{{L}^{-2}}\,{{T}^{4}}{{A}^{2}} \right]\] done
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B)
\[\left[ {{M}^{-1}}\,{{L}^{-1}}\,{{T}^{3}}\,{{A}^{1}} \right]\] done
clear
C)
\[\left[ {{M}^{-1}}\,{{L}^{-2\,}}\,{{T}^{4}}\,{{A}^{2}} \right]\] done
clear
D)
\[\left[ {{M}^{0}}\,{{L}^{-2}}\,{{T}^{4}}\,{{A}^{1}} \right]\] done
clear
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question_answer29)
Metallic sphere of radius R is charged to potential V. Then charge q is proportional to
A)
V done
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B)
R done
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C)
both V and R done
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D)
none of these. done
clear
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question_answer30)
If 64 identical spheres of charge q and capacitance C each are combined to form a large sphere. The charge and capacitance of the sphere is
A)
64 q, C done
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B)
16q, 4C done
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C)
64q, 4C done
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D)
16q, 64C done
clear
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question_answer31)
Directions: (31-35) |
Parallel Plate Capacitor |
The simplest and the most widely used capacitor is the parallel plate capacitor. It consists of two large plane parallel conducting plates, separated by a small distance. |
In the outer regions above the upper plate and below the lower plate, the electric fields due to the two charged plates cancel out. The net field is zero. |
In the inner region between the two capacitor plates, the electric fields due to the two charged plates add up. The net field is \[\frac{\sigma }{{{\varepsilon }_{0}}}\]. |
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For a uniform electric field, potential difference between the plates = Electric field \[\times \] distance between the plates. |
Capacitance of the parallel plate capacitor is, the charge required to be supplied to either of the conductors of the capacitor so as to increase the potential difference between them by unit amount. |
A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are
A)
Charge remains constant, potential decreases & capacitance increases done
clear
B)
Charge remains constant, potential increases & Capacitance decreases done
clear
C)
Charge increases, potential increases & Capacitance decreases done
clear
D)
Charge decreases, potential decreases & Capacitance increases. done
clear
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question_answer32)
In a parallel plate capacitor, the capacity increases if
A)
area of the plate decreases done
clear
B)
distance between the plates increases done
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C)
area of the plate increases done
clear
D)
dielectric constant decreases. done
clear
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question_answer33)
A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities on the plates are \[+\sigma \] and \[-\,\ sigma \]respectively. In the region between the plates the magnitude of the electric field is
A)
\[\frac{\sigma }{2{{\varepsilon }_{0}}}\] done
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B)
\[\frac{\sigma }{{{\varepsilon }_{0}}}\] done
clear
C)
0 done
clear
D)
none of these done
clear
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question_answer34)
If a parallel plate air capacitor consists of two circular plates of diameter 8 cm. At what distance should the plates be held so as to have the same capacitance as that of sphere of diameter 20 cm ?
A)
9 mm done
clear
B)
4 mm done
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C)
8 mm done
clear
D)
2 mm done
clear
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question_answer35)
If a charge of \[+2\centerdot 0\times {{10}^{-8}}\] is placed on the positive plate and a charge of \[-1\centerdot 0\times {{10}^{-8}}C\] on the negative plate of a parallel plate capacitor of capacitance \[1\centerdot 2\times {{10}^{-3}}\mu F\], then the potential difference developed between the plates is
A)
\[6\centerdot 25V\] done
clear
B)
\[3\centerdot 0V\] done
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C)
\[12\centerdot 5V\] done
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D)
25V done
clear
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question_answer36)
Directions: (36-40) |
Dielectric Slab |
A dielectric slab is a substance which does not allow the flow of charges through it but permits them, to exert electrostatic forces on one another. |
When a dielectric slab is placed between the plates, the field \[{{E}_{0}}\]polarises the dielectric. This induces charge \[-{{Q}_{p}}\] on the upper surface and \[+{{Q}_{p}}\]on the lower surface of the dielectric. These induced charges set up a field \[{{E}_{p}}\] inside the dielectric in the opposite direction of \[{{\overrightarrow{E}}_{0}}\] as shown. |
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In a parallel plate capacitor, the capacitance increases from \[4\,\mu F\] to \[80\,\mu F\], on introducing a dielectric medium between the plates. What is the dielectric constant of the medium?
A)
10 done
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B)
20 done
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C)
50 done
clear
D)
100 done
clear
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question_answer37)
A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The separation between the plates is now reduced half and the space between them is filled with a medium of dielectric constant 5. Calculate the value of capacitance of the capacitor in second case.
A)
8 pF done
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B)
10 pF done
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C)
80 pF done
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D)
100 pF done
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question_answer38)
A dielectric introduced between the plates of a parallel plate condenser
A)
decreases the electric field between the plates done
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B)
increases the capacity of the condenser done
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C)
increases the charge stored in the condenser done
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D)
increases the capacity of the condenser done
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question_answer39)
A parallel plate capacitor 1 pF has separation between the plates is d. When the distance of separation becomes 2d and wax of dielectric constant x is inserted in it, the capacitance becomes 2 pF. What is the value of x ?
A)
2 done
clear
B)
4 done
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C)
6 done
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D)
8 done
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question_answer40)
A parallel plate capacitor having area A and separated by distance a is filled by copper plate of thickness b. The new capacity is
A)
\[\frac{{{\varepsilon }_{0}}A}{d+\frac{b}{2}}\] done
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B)
\[\frac{{{\varepsilon }_{0}}A}{2d}\] done
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C)
\[\frac{{{\varepsilon }_{0}}A}{d-b}\] done
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D)
\[\frac{2{{\varepsilon }_{0}}A}{d+\frac{b}{2}}\] done
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question_answer41)
Directions: (41-45) |
Energy Stored in Capacitor |
A capacitor is a device to store energy. The process of charging up a capacitor involves the transferring of electric charges from its one place to another. This work done in charging the capacitor is stored as its electrical potential energy. |
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If q is the charge and V is the potential difference across a capacitor at any instant during its charging, then small work done in storing an additional small charge dq against the repulsion of charge q already stored on it is \[dW=V.dq=\left( q/C \right)dq\] |
A system of 2 capacitors of capacitance \[2\mu F\]and \[4\mu F\]is connected in series across a potential difference of 6 V. The energy stored in the system is
A)
\[3\mu J\] done
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B)
\[24\,\mu J\] done
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C)
\[30\,\mu J\] done
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D)
\[108\,\mu J\] done
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question_answer42)
A capacitor of capacitance of \[10\,\mu F\] is charged to 10 V. The energy stored in it is
A)
\[100\,\,\mu J\] done
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B)
\[500\,\mu J\] done
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C)
\[1000\,\mu J\] done
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D)
\[1\,\mu J\] done
clear
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question_answer43)
A parallel plate air capacitor has capacity C farad, potential V volt and energy E joule. When the gap between the plates is completely filled with dielectric
A)
both V and E increase done
clear
B)
both V and E decrease done
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C)
V decreases, E increases done
clear
D)
V increases, E decreases done
clear
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question_answer44)
A capacitor with capacitance \[5\,\mu F\] is charged to \[5\,\mu C\]. If the plates are pulled apart to reduce the capacitance to \[2\mu F\], how much work is done?
A)
\[6\centerdot 25\times {{10}^{-6}}J\] done
clear
B)
\[3\centerdot 75\times {{10}^{-6}}J\] done
clear
C)
\[2\centerdot 16\times {{10}^{-6}}J\] done
clear
D)
\[2\centerdot 55\times {{10}^{-6}}J\] done
clear
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question_answer45)
A metallic sphere of radius 18 cm has been given a charge of \[5\times {{10}^{-6}}\,C\]. The energy of the charged conductor is
A)
\[0\centerdot 2J\] done
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B)
\[0\centerdot 6J\] done
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C)
\[1\centerdot 2J\] done
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D)
\[2\centerdot 4J\] done
clear
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question_answer46)
A)
\[{{O}_{2}}\] done
clear
B)
\[{{H}_{2}}\] done
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C)
\[{{N}_{2}}\] done
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D)
\[HCl\] done
clear
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question_answer47)
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance
A)
increases K times done
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B)
remains unchanged done
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C)
decreases K times done
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D)
increases 2K times. done
clear
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question_answer48)
Which of the following is a dielectric?
A)
Copper done
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B)
Glass done
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C)
Antimony (Sb) done
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D)
None of these done
clear
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question_answer49)
For a polar molecule, which of the following statements is true?
A)
The centre of gravity' of electrons and protons Coincide done
clear
B)
The centre of gravity of electrons and protons do not coincide done
clear
C)
The charge distribution is always symmetrical done
clear
D)
The dipole moment is always zero done
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question_answer50)
When a comb rubbed with dry hair attracts pieces of paper. This is because the
A)
comb polarizes the piece of paper done
clear
B)
comb induces a net dipole moment opposite to the direction of field done
clear
C)
electric field due to the comb is uniform done
clear
D)
comb induces a net dipole moment perpendicular to the direction of field. done
clear
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