A charge q is to be distributed on two conducting spheres. What should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in the air?

1. $\frac{\mathrm{q}}{2} \mathrm{and} \frac{\mathrm{q}}{2}$

2. $\frac{\mathrm{q}}{2} \mathrm{and} \frac{3\mathrm{q}}{4}$

3. $\frac{\mathrm{q}}{3} \mathrm{and} \frac{2\mathrm{q}}{3}$

4. $\frac{\mathrm{q}}{5} \mathrm{and} \frac{4\mathrm{q}}{5}$

A point charge q₁ exerts an electric force on a second point charge q₂. If third charge q₃ is brought near, the electric force of q₁ exerted on q_2:

1. decreases.

2. increases.

3. remains unchanged.

4. increases if q₃ is of the same sign as q₁ and decreases if q₃ is of the opposite sign.

Three charges +4q, Q and q are placed in a straight line of length l at points 0, $\frac{\mathrm{l}}{2}$ and l distance away from one end respectively. What should be Q in order to make the net force on q to be zero?

1. -q

2. 4q

3. $-\frac{\mathrm{q}}{2}$

4. -2q

A particle of mass \(m\) carrying charge \(-q_1\) is moving around a charge \(+q_2\) along a circular path of radius \(r\). The period of revolution of the charge \(-q_1\) is:
1. \(\sqrt{\frac{16\pi^{3} \varepsilon_{0} mr^{3}}{q_{1} q_{2}}}\)
2. \(\sqrt{\frac{8\pi^{3} \varepsilon_{0} mr^{3}}{q_{1} q_{2}}}\)
3. \(\sqrt{\frac{q_{1} q_{2}}{16 \pi^{3} \varepsilon_{0} mr^{3}}}\)
4. zero

Consider three point objects P, Q and R. P and Q repel each other while P and R attract each other. What is the nature of force between Q and R?

1. Repulsive force

2. Attractive force

3. No force

4. None of these

The electric field intensity at a point in a vacuum is equal to:

1. zero

2. the force a proton would experience there.

3. the force an electron would experience there.

4. the force a unit positive charge would experience there.

A sphere of radius r has an electric charge uniformly distributed in its entire volume. At a distance d from the centre inside the sphere (d<r) the electric field intensity is directly proportional to:

1. $\frac{1}{\mathrm{d}}$

2. $\frac{1}{{\mathrm{d}}^2}$

3. d

4. ${\mathrm{d}}^2$

The electric field at a distance 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance $\frac{\mathrm{R}}{2}$ from the centre will be:

1. Zero

2. 2E

3. 4E

4. 16E

In a uniform electric field if a charge is fired in a direction different from the line of the electric field, then the trajectory of the charge will be a:

1. straight line

2. circle

3. parabola

4. ellipse

A positively charged pendulum is oscillating in a uniform electric field pointing upwards. Its time period as compared to that when it oscillates without electric field:

1. is less.

2. is more.

3. remains unchanged.

4. starts fluctuating.