Electric potential at any point is $V=-5x+3y+\sqrt{15}z$, then the magnitude of the electric field is

(1) $3\sqrt{2}$

(2) $4\sqrt{2}$

(3) $5\sqrt{2}$

(4) 7

Kinetic energy of an electron accelerated in a potential difference of 100 V is 

(1) 1.6 × 10^–17 J

(2) 1.6 × 10²¹ J

(3) 1.6 × 10^–29 J

(4) 1.6 × 10^–34 J

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. $\frac{(q+Q)}{4\pi {\epsilon }_0}\frac{2}{R}$

2. $\frac{2Q}{4\pi {\epsilon }_{0}R}$

3. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$

4. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

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