A total charge \(Q\) is broken in two parts \(Q_1\) and \(Q_2\) and they are placed at a distance \(R\) from each other. The maximum force of repulsion between them will occur, when:

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:

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
\(\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\right)\)

Four charges are arranged at the corners of a square \(ABCD\) as shown in the figure. The force on a positive charge kept at the center of the square is:

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

Three charges are placed at the vertices of an equilateral triangle of side \(a\) as shown in the following figure. The force experienced by the charge placed at the vertex \(A\) in a direction normal to \(BC\) is: 

1. \(Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

2. \(- Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

3. zero

4. \(Q^{2} / \left(\right. 2 \pi \epsilon_{0} a^{2} \left.\right)\)

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

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. \(10^{-20}~\text{C}\)