A coil of 100 turns, radius 5cm carries a current of 0.1 A. It is placed in a magnetic field of 1.5 T initially with its plane perpendicular to the field. The work done to rotate it through on angle of ${180}^0 \mathrm{is}... \times {10}^{-3} \mathrm{J}$.

Given data

Number of turns=100

Radius r=5cm

Current i=0.1 A 

Magnetic field B=1.5 T

Angle =180 degrees

Concepts used moving charges and magnetism

Explanation

The work done through the rotating angle is

$$\begin{gathered} W=\Delta U \\ W=MB\cos {\theta }_1-\cos {\theta }_2 \end{gathered}$$

Where angle =180

M=NIA

Therefore the required equation is

$W=\frac{NIBA}{2}$

Substitute the given values we get

$W=\frac{100\times 0.1\times 1.5\times \pi \times 5^2}{2}$

By solving we get

$W=75\pi \times {10}^{-3}$