Two equally charged identical small balls kept at some fixed distance apart exert a repulsive force F on each other. A similar uncharged ball, after touching one of them is placed at the mid-point of the line joining the two balls. The force experienced by the third ball is: 

1. 4F

2. 2F

3. F

4. $\frac{\mathrm{F}}{16}$

Two equal point charges A and B are R distance apart. A third point charge placed on the perpendicular bisector at a distance d from the centre will experience a maximum electrostatic force when:

1. $\mathrm{d}=\frac{\mathrm{R}}{2\sqrt{2}}$

2. $\mathrm{d}=\frac{\mathrm{R}}{\sqrt{2}}$

3. $\mathrm{d}=\mathrm{R}\sqrt{2}$

4. $\mathrm{R}=2\sqrt{2}\mathrm{R}$

A charged gold leaf electroscope has its leaves apart by a certain amount of having enclosed air. When the electroscope is subjected to X-rays, then the leaves:

1. Further dilate

2. Start oscillating

3. Collapse

4. Remain unaltered

Two equal positive charges Q are fixed at points (a, 0) and (-a, 0) on the x-axis. An opposite charge -q at rest is released from point (0, a) on the y-axis. The charge -q will

1. move to infinity.

2. move to the origin and rest there.

3. undergo SHM about the origin.

4. execute oscillatory periodic motion but not SHM.

Four charges each equal to Q are placed at the four corners of a square and a charge q is placed at the centre of the square. If the system is in equilibrium then the value of q is:

1. $\frac{\mathrm{Q}}{2}(1+2\sqrt{2})$

2. $\frac{-\mathrm{Q}}{4}(1+2\sqrt{2})$

3. $\frac{\mathrm{Q}}{4}(1+2\sqrt{2})$

4. $\frac{-\mathrm{Q}}{2}(1+2\sqrt{2})$

According to Coulomb's Law, which is the correct relation for the following diagram?

1. ${\mathrm{q}}_1{\mathrm{q}}_2<0$

2. ${\mathrm{q}}_1{\mathrm{q}}_2>0$

3. ${\mathrm{q}}_1{\mathrm{q}}_2=0$

4. ${\mathrm{q}}_1{\mathrm{q}}_2>>100\mathrm{C}$

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