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:

Force of attraction between two point charges Q and – Q separated by d meter is F_e. When these charges are given to two identical spheres of radius R = 0.3 d whose centres are d meter apart, the force of attraction between them is 

1. Greater than F_e

2. Equal to F_e

3. Less than F_e

4. None of the above

A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q. The surface charge density on the inner and outer surfaces of the spherical shell will be?

(1) $-\frac{2\mathrm{Q}}{4{\mathrm{\pi b}}^2}, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(2) $-\frac{\mathrm{Q}}{4{\mathrm{\pi b}}^2}, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(3) $0, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(4) None of the above

Two particles of equal mass \(m\) and charge \(q\) are placed at a distance of \(16~\text{cm}\). They do not experience any net force. The value of \(\frac{q}{m}\) is: 
1. \(l\)
2. \(\sqrt{\frac{\pi \varepsilon_0}{G}}\)
3. \(\sqrt{\frac{G}{4\pi \varepsilon_0}}\)
4. \(\sqrt{4\pi \varepsilon_0 G}\)

\(ABC\) is an equilateral triangle. Charges \(+q\)  are placed at each corner. The electric intensity at \(O\) will be: 

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests 

(1) E_A > E_B > E_C

(2) E_A = E_B = E_C

(3) E_A = E_C > E_B

(4) E_A = E_C < E_B

A hollow insulated conducting sphere is given a positive charge of 10μC. What will be the electric field at the centre of the sphere if its radius is 2 meters 

(1) Zero

(2) 5 μCm^–2

(3) 20 μCm^–2

(4) 8 μCm^–2

Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then:

(1) only -q is in stable equilibrium.

(2) none of the charges are in equilibrium.

(3) all the charges are in unstable equilibrium.

(4) all the charges are in stable equilibrium.