Question

The magnetic potential at a point on the axial line of a bar magnet of dipole moment $$ M $$ is $$ V. $$ What is the magnetic potential due to a bar magnet of dipole moment $$ \frac{M}{4} $$ at the same point

Answer 1

Correct option is D. $$ \frac{V}{4} $$

Magnetic potential at a distance $$ d $$ from the bar magnet on it's axial line is given by

$$ V=\dfrac{\mu_0}{4 \pi}. \dfrac{M}{d^2} \Rightarrow V \propto M \Rightarrow \dfrac{V_1}{V_2}=\dfrac{M_1}{M_2} $$

$$ \Rightarrow \dfrac{V}{V_2}=\dfrac{M}{M/4} \Rightarrow V_2 = \dfrac{V}{4} $$