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.

An infinite number of charges, each of charge 1 μC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ....∞. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge?

Three identical positive point charges, as shown are placed at the vertices of an isosceles right-angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point M of the hypotenuse?
                
1. 1
2. 2
3. 3
4. 4

An electron enters an electric field with its velocity in the direction of the electric lines of force. Then: 

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

1. sin θ

2. tan θ

3. cos θ

4. cot θ

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:

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. ${180}^o,$ $\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{{\left(2L\right)}^2}$

2. ${90}^o,$ $\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{L^2}$

3. ${180}^o,$ $\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{2L^2}$

4. ${180}^o,$ $\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{L^2}$ 

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:

The electrostatic field due to a charged conductor just outside the conductor is:

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 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. \(10^{-20}~\text{C}\)