Question

A magnetic needle lying parallel to the magnetic field required W units of work to turn it through an angle 45${}^o$. The torque required to maintain the needle in this position will be

• A. $\sqrt{2}W$
• B. $\frac{1}{\sqrt{3}W}$
• C. $(\sqrt{2}-1)W$
• D. $\frac{W}{(\sqrt{2}-1)}$

Answer 1

The correct option is D $\frac{W}{(\sqrt{2}-1)}$

Work done to turn magnetic needle (lying parallel to magnetic field) through 45 degree is
$W=MB(1-\cos 45)=MB(1-\frac{1}{\sqrt{2}})$
M is the magnetic dipole moment and B is the magnetic field.
$MB=\frac{\sqrt{2}W}{(\sqrt{2}-1)}$
Torque required to maintain the position is $\tau =MB\sin 45=\frac{W}{(\sqrt{2}-1)}$