A thin spherical conducting shell of radius \(R\) has a charge \(q.\) Another charge \(Q\) is placed at the centre of the shell. The electrostatic potential at a point \(P\) which is at a distance \(\frac{R}{2}\) from the centre of the shell is:
1. \(\frac{\left( q + Q \right)}{4 \pi \varepsilon_{0}} \frac{2}{R}\)
2. \(\frac{2 Q}{4 \pi \varepsilon_{0} R}\)
3. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} - \frac{2 q}{4 \pi \varepsilon_{0} R}\)
4. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} + \frac{q}{4 \pi \varepsilon_{0} R}\)

Subtopic:  Electric Potential |
 62%
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A charge of \(10\) e.s.u. is placed at a distance of \(2\) cm from a charge of \(40\) e.s.u. and \(4\) cm from another charge of \(20\) e.s.u. The potential energy of the charge \(10\) e.s.u. is: (in ergs) 

1. \(87.5\) 2. \(112.5\)
3. \(150\) 4. \(250\)
Subtopic:  Electric Potential Energy |
 58%
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A sphere of 4 cm radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged to potential 3 e.s.u. and the outer sphere is earthed. The charge on the inner sphere is 

(1) 54 e.s.u.

(2) 14 e.s.u.

(3) 30 e.s.u.

(4) 36 e.s.u.

Subtopic:  Electric Potential |
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When one electron is taken towards the other electron, then the electric potential energy of the system -

(1) Decreases

(2) Increases

(3) Remains unchanged

(4) Becomes zero

Subtopic:  Electric Potential Energy |
 76%
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Four charges +Q,Q,+Q,Q are placed at the corners of a square taken in order. At the centre of the square 

(1) E=0,V=0

(2) E=0,V0

(3) E0,V=0

(4) E=0,V0

Subtopic:  Electric Potential |
 58%
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Point charge q1 = 2 μC and q2 = –1 μC are kept at points x = 0 and x = 6 respectively. Electrical potential will be zero at points 

(1) x = 2 and x = 9

(2) x = 1 and x = 5

(3) x = 4 and x = 12

(4) x = –2 and x = 2

Subtopic:  Electric Potential |
 71%
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Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction are 

(1) Planes parallel to yz-plane

(2) Planes parallel to xy-plane

(3) Planes parallel to xz-plane

(4) Coaxial cylinders of increasing radii around the x-axis

Subtopic:  Equipotential Surfaces |
 75%
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A bullet of mass 2 gm is having a charge of 2 μC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s ?

(1) 5 kV

(2) 50 kV

(3) 5 V

(4) 50 V

Subtopic:  Electric Potential Energy |
 84%
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In a certain charge distribution, all points having zero potential can be joined by a circle \(S\). Points inside \(S\) have positive potential, and points outside \(S\) have a negative potential. A positive charge, which is free to move, is placed inside \(S\). What is the correct statement about \(S\):

1. It will remain in  equilibrium 2. It can move inside \(S\), but it cannot cross \(S\)
3. It must cross \(S\) at some time 4. It may move, but will ultimately return to its starting point
Subtopic:  Equipotential Surfaces |
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A square of side ‘a’ has charge Q at its centre and charge ‘q’ at one of the corners. The work required to be done in moving the charge ‘q’ from the corner to the diagonally opposite corner is -

(1) Zero

(2) Qq4π0a

(3) Qq24π0a

(4) Qq2π0a

Subtopic:  Electric Potential |
 72%
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