A charge q is to be divided on two small conducting spheres. What should be the value of charges on the spheres so that when placed at a certain distance apart, the repulsive force between them is maximum?

1. $\frac{q}{4} and \frac{3q}{4}$

2. $\frac{q}{2} and \frac{q}{2}$

3. $\frac{q}{3} and \frac{q}{3}$

4. $\frac{q}{4} and \frac{q}{4}$

An electric dipole of dipole moment p is placed in an electric field of intensity E such that angle between electric field and dipole moment is $\theta$. Assuming that the potential energy of the dipole is zero when $\theta =0°$, the potential energy of the dipole will be

(1) -pE cos$\theta$

(2) pE(1-cos$\theta$)

(3) pE(cos$\theta$-1)

(4) -2pE(cos$\theta$-1)

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

A particle having charge ${\mathrm{q}}_1$ exerts F electrostatic force on charge ${\mathrm{q}}_2$ at rest. If a particle having charge $\frac{q_1}{4}$ is placed midway between the line joining the two charges ${\mathrm{q}}_1 \mathrm{and} {\mathrm{q}}_2$ then electrostatic force on ${\mathrm{q}}_2$ due to ${\mathrm{q}}_1$ will become/remain

1. 2F

2. $\frac{F}{2}$

3. F

4. zero

A particle of mass m and charge q is at rest. If it is moved with velocity $\frac{\sqrt{3}c}{2}$ where c is speed of light in vacuum, then its charge will become/remain

(1) 2q

(2) $\sqrt{3}q$

(3) $\frac{q}{2}$

(4) q

An electric dipole is in unstable equilibrium in the uniform electric field. The angle between its dipole moment and the electric field is

1.  90$°$

2.  120$°$

3.  0$°$

4.  180$°$

The law, governing the force between electric charges is known as 

(1) Ampere's law

(2) Ohm's law

(3) Faraday's law

(4) Coulomb's law

F_g and F_e represents gravitational and electrostatic force respectively between electrons situated at a distance 10 cm. The ratio of F_g/ F_e is of the order of 

(1) 10⁴²

(2) 10

(3) 1

(4) 10^–43

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

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