A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is

Question

A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is (A)  60°  (B)  45°  (C)  30°  (D)  75°

Tardigrade Admin · Accepted Answer

τ = MB sin θ where θ=90° ∴ τ-MB Given τ2=(1/2)τ1 ∴ MB sinθ=(1/2)MB ∴ sin θ=(1/2) ⇒ θ=30° Angle of rotation is = 90°-30°=60°

Q. A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is

$6 0^{\circ}$

$4 5^{\circ}$

$3 0^{\circ}$

$7 5^{\circ}$

$τ = MB sin θ$
where $θ = 9 0^{\circ}$
$∴ τ - MB$
Given $τ_{2} = \frac{1}{2} τ_{1}$
$∴ MB sin θ = \frac{1}{2} MB$
$∴ sin θ = \frac{1}{2}$
$\Rightarrow θ = 3 0^{\circ}$
Angle of rotation is = $9 0^{\circ} - 3 0^{\circ} = 6 0^{\circ}$