For a short dipole placed at origin O , the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V₀ and E₀, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by

Solution

Physics sir · 4 steps

A is on the dipole's axis and B is on its equator: compare the two formulas, then scale by distance.

1. Where the points sit. The dipole points along x, so A at distance r is on the axial line. B at distance 2r on the y-axis is on the equatorial line.
2. Values at A. On the axis, V₀ = kp/r² and E₀ = 2kp/r³, where k = 1/4πε₀.
3. Potential at B. Every point on the equatorial line is equally far from +q and -q, so their potentials cancel. That gives V_B = 0.

   E_B = kp/(2r)³ = kp/8r³ = 1/16·2kp/r³ = E₀/16

4. So. At B the potential is zero and the field is E₀/16, which is option (d).

The idea to keep. For a short dipole, the axial field is twice the equatorial field at the same distance, and the field falls as 1/r³. The potential on the equatorial line is always zero.

Answer from the NTA final answer key. Solution by PrepWiser.