In the absence of other conductors, the surface charge density

(1) Is proportional to the charge on the conductor and its surface area

(2) Inversely proportional to the charge and directly proportional to the surface area

(3) Directly proportional to the charge and inversely proportional to the surface area

(4) Inversely proportional to the charge and the surface area

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.