Question

A short bar magnet with its north pole facing geographic north forms a neutral point at $P$ in the horizontal plane. If the magnet is rotated by $90^{\circ}$ in the horizontal plane, the net magnetic induction at $P$ is (Horizontal component of earth's magnetic field $=B_{H}$ )

• A. 0
• B. $2 B_{H}$
• C. $\frac{\sqrt{5}}{2} B_{H}$
• D. $\sqrt{5} B_{H}$

Answer 1

Answer: (D)

Initially

Neutral point is obtained on equatorial line and at neutral point $\left|B_{H}\right|=\left| B_{e}\right|$
where $B_{H}=$ Horizontal component of earth's magnetic field, $B_{e}=$ Magnetic field due to bar magnet on its equatorial line

Finally
Point $P$ comes on axial line of the magnet and at $P$,
Net magnetic field $B=\sqrt{B_{a}^{2}+V_{H}^{2}}$
$=\sqrt{\left(2 B_{e}\right)^{2}+\left(B_{H}\right)^{2}}$
$=\sqrt{\left(2 B_{H}\right)^{2}+B_{H}^{2}}=\sqrt{5} B_{H}$