If the force acting on a point charge kept on the axis of an electric dipole is F, what will be the amount of force if the distance of the point charge is doubled from the dipole?a)2Fb)F/8c)F/2d)F/4Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Force acting on a point charge kept on the axis of an electric dipole = F

To find:
The amount of force if the distance of the point charge is doubled from the dipole

Solution:
Let's consider the electric dipole as two equal and opposite point charges +q and -q separated by a distance d.

The electric field at a point on the axial line of the dipole is given by:
E = (1/4πε₀) * (2qd / r³)

where ε₀ is the permittivity of free space, q is the magnitude of each charge, d is the separation between the charges, and r is the distance of the point from the center of the dipole.

The force experienced by a point charge q₀ placed at a distance r from the center of the dipole is given by:
F = q₀ * E

Substituting the expression for E in terms of q and d, we get:

F = (1/4πε₀) * (2q*q₀d / r³)

Now, if the distance of the point charge is doubled from the dipole, i.e. r → 2r, then the force experienced by the charge will be:

F' = (1/4πε₀) * (2q*q₀d / (2r)³)

F' = (1/4πε₀) * (2q*q₀d / 8r³)

F' = F/8

Therefore, the amount of force if the distance of the point charge is doubled from the dipole is F/8.

Hence, the correct answer is option B.

Answer

If the distance of a point charge, kept on the axis of a dipole, is sufficiently large than the separation between the charges of a dipole, then it can be shown that electric field E at a distance r from the dipole varies as E α 1/(r³). Now if the distance becomes 2r, electric field intensity will decrease by a factor of 2³= 8 times. Therefore the force F will now become F/8.

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