Question

A short magnet produces a deflection of 30° when placed at certain distance in tanA position of magnetometer. If another short magnet of double the length and thrice the pole strength is placed at the same distance in tanB position of the magnetometer, the deflection produced will be:

Options

• 60°

• 30°

• 45°

• None of these

Answer 1

60°

Explanation:

In tan A position,

${\displaystyle \frac{{\mu }_0}{4\pi }\frac{2\text{M}}{{\text{d}}^3}={\text{B}}_{\text{H}}}$ tan 30° = ${\displaystyle \frac{{\text{B}}_{\text{H}}}{\sqrt{3}}}$   ...(1)

Magnetic moment of second magnet,

M' = (3m)(2 × 2ℓ) = 6M

In tan B position,

${\displaystyle \frac{{\mu }_0}{4\pi }\frac{6\text{M}}{{\text{d}}^3}}$ = B_H tanθ     ...(2)

Dividing eq. (2) by (1) we get

${\displaystyle \frac{6}{2}=\frac{\tan \theta }{1/\sqrt{3}}}$ or tanθ = ${\displaystyle \sqrt{3}}$

or θ = 60°