The distance of the field point on the axis of a small electric dipole is doubled. By what factor will the electric field due to the dipole change

Question

Answer

Explanation

When the distance of the field point on the axis of a small electric dipole is doubled, the electric field due to the dipole changes by a factor of 4.

Reasoning

To understand why the electric field due to the dipole changes by a factor of 4, we need to examine the equation for the electric field due to a dipole.

The electric field due to a dipole at a point on its axis is given by the equation:

E = (2kp/r^3) * p

where E is the electric field, p is the dipole moment, r is the distance between the dipole and the point, and k is the Coulomb constant.

If the distance of the field point on the axis of the dipole is doubled, the new distance becomes 2r. To find the new electric field, we substitute 2r for r in the above equation:

E' = (2kp/(2r)^3) * p
= (2kp/8r^3) * p
= (kp/r^3) * (p/4)
= (1/4) * E

The new electric field is one-fourth the original electric field. Therefore, the electric field due to the dipole changes by a factor of 4 when the distance of the field point on the axis of the dipole is doubled.

Answer

For a short dipole,
electric field at an axial position is inversely proportional to the third power of distance b/w the centre of dipole and the point!!!

so, if the distance is doubled, electric field will reduce with a factor of 1/8 th times.

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