Two spherical conductors \(B\) and \(C\) having equal radii and carrying equal charges in them repel each other with a force \(F\) when kept apart at some distance. A third spherical conductor having same radius as that of \(B\) but uncharged is brought in contact with \(B\), then brought in contact with \(C\) and finally removed away from both. The new force of repulsion between \(B\) and \(C\) is:
1. \(\frac{F}{4}\)
2. \(3\frac{F}{4}\)
3. \(\frac{F}{8}\)
4. \(3\frac{F}{8}\)

Two identical conductors of copper and aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminium will be:

1. zero.

2. greater than in copper.

3. equal to that in copper.

4. less than in copper.

A large non-conducting sheet S is given a uniform charge density. Two uncharged small, metal rods A and B are placed near the sheet as shown in the following diagram. Choose the incorrect option:

1.  S attracts A.

2.  S attracts B.

3.  A attracts B.

4.  S repels A.

Five balls numbered \(1\) to \(5\) are suspended using separate threads. Pairs \((1, 2), (2, 4),\) and \((4, 1)\) show electrostatic attraction, while pairs \((2, 3)\) and \((4, 5)\) show repulsion. Therefore ball \((1)\) must be:

1. positively charged
2. negatively charged
3. neutral
4. made of metal

Two small spheres each having the charge \(+Q\) are suspended by insulating threads of length \(L\) from a hook. If this arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be:

1. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{(2 L )^{2}}\)

2. \(90^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{(L )^{2}}\)

3. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{2 L ^{2}}\)

4. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{ L ^{2}}\) 

Two charges \(+2\) C and \(+6\) C are repelling each other with a force of \(12\) N. If each charge is given \(-2\) C of charge, then the value of the force will be:

Suppose the charge of a proton and an electron differ slightly. One of them is \(-e,\) the other is \((e+\Delta e).\) If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then \(\Delta e\) is of the order of?
(Given the mass of hydrogen ${\mathrm{}}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)$$)
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)

Two positive ions, each carrying a charge \(q\), are separated by a distance \(d\). If \(F\) is the force of repulsion between the ions, the number of electrons missing from each ion will be:
(\(e\) is the charge on an electron)