If identical charges (–q) are placed at each corner of a cube of side b, then electric potential energy of charge (+q) which is placed at centre of the cube will be -

(1) $\frac{8\sqrt{2}{q}^2}{4\pi {\epsilon }_{0}b}$

(2) $\frac{-8\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$

(3) $\frac{-4\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$

(4) $\frac{-4q^2}{\sqrt{3}\pi {\epsilon }_{0}b}$

A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be -

(1) 1840 keV

(2) 1/1840 keV

(3) 1 keV

(4) 920 keV

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. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} + \frac{q}{4 \pi \varepsilon_{0} R}\)

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) 

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) $\frac{1}{4}$ e.s.u.

(3) 30 e.s.u.

(4) 36 e.s.u.

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

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) $E=0,V\ne 0$

(3) $E\ne 0,V=0$

(4) $E=0,V\ne 0$

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

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

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