A magnet of magnetic moment M is lying in a magnetic field of induction B . W1 is the work done in turning it from 0° to 60° and W2 is the work done in turning it from 30° to 90°. Then

Question

A magnet of magnetic moment M is lying in a magnetic field of induction B . W1 is the work done in turning it from 0° to 60° and W2 is the work done in turning it from 30° to 90°. Then (A) W2=(W1/2) (B) W2=2 W1 (C) W2=W1 (D) W2=√3 W1

Tardigrade Admin · Accepted Answer

As W=-M B( cos θ2- cos θ1) W1=-M B[ cos 60°- cos 0°]=-M B((1/2)-1)=(M B/2) W2=-M B( cos 90°- cos 30°)=-M B(0-(√3/2))=(√3 M B/2) W2=√3 W1

Q. A magnet of magnetic moment $M$ is lying in a magnetic field of induction $B . W_{1}$ is the work done in turning it from $0^{\circ}$ to $6 0^{\circ}$ and $W_{2}$ is the work done in turning it from $3 0^{\circ}$ to $9 0^{\circ}$ . Then

$W_{2} = \frac{W _{1}}{2}$

$W_{2} = 2 W_{1}$

$W_{2} = W_{1}$

$W_{2} = 3 W_{1}$

As $W = - MB (cos θ_{2} - cos θ_{1})$
$W_{1} = - MB [cos 6 0^{\circ} - cos 0^{\circ}] = - MB (\frac{1}{2} - 1) = \frac{MB}{2}$
$W_{2} = - MB (cos 9 0^{\circ} - cos 3 0^{\circ}) = - MB (0 - \frac{3}{2}) = \frac{3 MB}{2}$
$W_{2} = 3 W_{1}$

Q. A magnet of magnetic moment M is lying in a magnetic field of induction B.W1​ is the work done in turning it from 0∘ to 60∘ and W2​ is the work done in turning it from 30∘ to 90∘. Then

W2​=2W1​​

W2​=2W1​

W2​=W1​

W2​=3​W1​