A bar magnet is held at a right angle 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 a right angle 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

Torque, τ=MBsin θ Where θ =90° ∴ τ=MB Given, τ2=(1/2 )τ1 ∴ MB sin θ =(1/2) MB ∴ sin θ = (1/2) ⇒ θ =30° Angle of rotation =90° -30° =60°

Q. A bar magnet is held at a right angle 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

$6 0^{\circ}$

$4 5^{\circ}$

$3 0^{\circ}$

$7 5^{\circ}$

Torque, $τ = MB s in θ$
Where $θ = 9 0^{\circ}$
$∴ τ = MB$
Given, $τ_{2} = \frac{1}{2} τ_{1}$
$∴ MB s in θ = \frac{1}{2} MB$
$∴ s in θ = \frac{1}{2}$
$\Rightarrow θ = 3 0^{\circ}$
Angle of rotation $= 9 0^{\circ} - 3 0^{\circ} = 6 0^{\circ}$