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 ${\mathrm{q}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{q}}_2$ 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 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. $\frac{q}{4}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\frac{3q}{4}$

2. $\frac{q}{2}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\frac{q}{2}$

3. $\frac{q}{3}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\frac{q}{3}$

4. $\frac{q}{4}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\frac{q}{4}$

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:

Out of gravitational, electromagnetic, Vander Waals, electrostatic and nuclear forces; which two are able to provide an attractive force between two neutrons 

(1) Electrostatic and gravitational

(2) Electrostatic and nuclear

(3) Gravitational and nuclear

(4) Some other forces like Vander Waals

Three charges \(4q,Q,\) and \(q\) are in a straight line in the position of \(0,l/2,\) and \(l\) respectively. The resultant force on \(q\) will be zero if \(Q\) equal to:
1. \(-q\)
2. \(-2q\)
3. \(\frac{-q}{2}\)
4. \(4q\)

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 each of 1 coulomb are at a distance 1 km apart, the force between them is 

(1) 9 × 10³ Newton

(2) 9 × 10^–3 Newton

(3) 1.1 × 10^–4 Newton

(4) 10⁴ Newton

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: