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