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
Distance of the point charge from the dipole = d
If the distance of the point charge is doubled from the dipole, then the new distance = 2d

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

Solution:
Electric dipole is a pair of equal and opposite charges separated by a distance 'd'. The direction of the dipole moment is from negative to positive charge.

The electric field due to an electric dipole at a point on its axial line at a distance 'r' from the center of the dipole is given by:

E = 2kp/(r^3)

where k is the Coulomb constant, p is the magnitude of the electric dipole moment and r is the distance from the center of the dipole.

The force experienced by a point charge 'q' placed in an electric field 'E' is given by:

F = qE

In this case, the force acting on the point charge due to the electric field of the dipole is given by:

F = q * 2kp/(d^3)

When the distance of the point charge is doubled from the dipole, the new distance becomes 2d. The electric field due to the dipole at this new distance is given by:

E' = 2kp/(8d^3) = kp/(4d^3)

The force experienced by the point charge at this new distance is given by:

F' = q * kp/(4d^3)

Therefore, the ratio of the new force to the original force is:

F'/F = (q * kp/(4d^3)) / (q * 2kp/(d^3)) = 1/8

Hence, the amount of force when the distance of the point charge is doubled from the dipole is F/8. Therefore, the correct option is 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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