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:

The dielectric constant of pure water is 81. Its permittivity will be:

1. 7.12 × 10^–10 MKS units

2. 8.86 × 10^–12 MKS units

3. 1.02 × 10¹³ MKS units

4. Cannot be calculated

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

One metallic sphere A is given a positive charge whereas another identical metallic sphere B of the exact same mass as of A is given an equal amount of negative charge. Then:

(1) mass of A and mass of B are the same.

(2) mass of A is more.

(3) mass of B is less.

(4) mass of B is more.

Two charges each equal to 2μC are 0.5m apart. If both of them exist inside the vacuum, then the force between them is 

(1) 1.89 N

(2) 2.44 N

(3) 0.144 N

(4) 3.144 N