Two spheres of electric charges + 2 nC and −8 nC are placed at a distance d apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before ?

• d

• $\frac{\mathrm{d}}{2}$

• $\frac{3\mathrm{d}}{4}$

• $\frac{4\mathrm{d}}{3}$

Three point charges of + 2q, + 2q and − 4q are placed at the corners A, B and C of an equilateral triangle ABC of side x. The magnitude of the electric dipole moment of this system is

• 2qx

• $3\sqrt{2} \mathrm{qx}$

• 3qx

• $2\sqrt{3} \mathrm{qx}$

64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with of the big drop is

• 64 : 1

• 1 : 64

• 1 : 4

• 4 : 1

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting. Then the system

• will be in equilibrium if the charges rotate about the centre of the triangle

• can never be in equilibrium

• will be in equilibrium if the charges have the same magnitudes but different sign

• will be in equilibrium if the charges have different magnitude and different signs.

105.

Two copper balls, each weighing 10 g are kept in air 10 cm apart. If one electron from every 10⁶ atoms is transferred from one ball to the other, the Coulomb force between them is (atomic weight of copperis 63.5)

• 2.0 × 10⁴ N

• 2.0 × 10¹⁰ N

• 2.0 × 10⁶ N

• 2.0 × 10⁶ N

The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field will be given by

In a coil of resistance 10Ω, the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in weber is 

• 8

• 2

• 6

• 6

What is the flux through a cube of side a if a point charge of q is a one of its corner?

Two thin dielectric slabs of dielectric constants K₁ and K₂ (K₁ < K₂) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by:

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

• zero and 

• 

• 

•