Question

In the given figure, the axial magnetic field at a point $P$, at a distance $r$ from the centre $O$ of a solenoid is (Consider $m$ as the magnitude of the magnetic moment of the solenoid).

• A. $B=\frac{2 \mu_{0}}{3 \pi} \frac{2 m}{r^{3}}$
• B. $B=\frac{4}{3} \frac{\mu_{0}}{\pi} \frac{2 m}{r^{3}}$
• C. $B=\frac{\mu_{0}}{4 \pi} \frac{2 m}{r^{3}}$
• D. $B=\frac{\mu_{0}}{2 \pi} \frac{2 m}{r^{3}}$

Answer 1

Answer: (C)

Magnitude of the magnetic moment of the solenoid is,
$m=n(2 l) I\left(\pi a^{2}\right)$
Thus, $B=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{r^{3}}$