Two small spherical balls each carrying a charge Q = 10 μC (10 micro-coulomb) are suspended by two insulating threads of equal lengths 1m each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle 60° between them, as shown in the figure. What is the tension in the threads (Given: $\frac{1}{\left(4\pi {\epsilon }_0\right)}=9\times {10}^{9}Nm/C^2$) 

(1) 18 N

(2) 1.8 N

(3) 0.18 N

(4) None of the above

An electron having charge \(e\) and mass \(m\) is moving in a uniform electric field \(E.\) Its acceleration will be:
1. \(\frac{e^2}{m}\)
2. \(\frac{E^2e}{m}\)
3. \(\frac{eE}{m}\)
4. \(\frac{mE}{e}\)

If an insulated non-conducting sphere of radius R has charge density ρ. The electric field at a distance r from the centre of sphere (r < R) will be 

(1) $\frac{\rho R}{3{\epsilon }_0}$

(2) $\frac{\rho r}{{\epsilon }_0}$

(3) $\frac{\rho r}{3{\epsilon }_0}$

(4) $\frac{3\rho R}{{\epsilon }_0}$ 

Infinite charges of magnitude q each are lying at x =1, 2, 4, 8... meter on X-axis. The value of the intensity of the electric field at point x = 0 due to these charges will be 

(1) 12 × 10⁹q N/C

(2) Zero

(3) 6 × 10⁹q N/C

(4) 4 × 10⁹q N/C

A pendulum bob of mass $30.7\times {10}^{-6}kg$ and carrying a charge $2\times {10}^{-8}C$ is at rest in a horizontal uniform electric field of 20000 V/m. The tension in the thread of the pendulum is $(g=9.8m/s^2)$

(1) $3\times {10}^{-4}N$

(2) $4\times {10}^{-4}N$

(3) $5\times {10}^{-4}N$

(4) $6\times {10}^{-4}N$ 

A charged ball \(B\) hangs from a silk thread \(S,\) which makes an angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to: 

1. \(\sin\theta\)
 2. \(\tan\theta\)
 3. \(\cos\theta\)
 4. \(\cot\theta\)

Two-point charges +8q and –2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is 

1. 8 L

2. 4 L

3. 2 L

4. $\frac{L}{4}$

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point P is 

(1) $\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(2) $-\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(3) $\frac{4\sigma }{{\epsilon }_o}\hat{k}$

(4) $-\frac{4\sigma }{{\epsilon }_o}\hat{k}$

Four-point +ve charges of the same magnitude (Q) are placed at four corners of a rigid square frame as shown in the figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a distance z away from the above frame (z<<L) then 

1. – ve charge oscillates along the Z-axis.

2. It moves away from the frame.

3. It moves slowly towards the frame and stays in the plane of the frame.

4. It passes through the frame only once.