Question

The rectangular coil having $100$ turns is placed in a uniform magnetic field of $\frac{0.05}{\sqrt{2}}\hat{j}\text{T}$ as shown in figure. Find the torque acting on the loop.

• A. $10\times {10}^{-3}\hat{k}\text{Nm}$
• B. $5.66\times {10}^{-3}\hat{k}\text{Nm}$
• C. $5.66\times {10}^{-3}\hat{i}\text{Nm}$
• D. $10\times {10}^{-3}\hat{i}\text{Nm}$

Answer 1

The correct option is B $5.66\times {10}^{-3}\hat{k}\text{Nm}$

Torque acting on the rectangular coil $$\overrightarrow{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}$$For $N$turns magnetic moment of the current carrying coil is given by, $\overrightarrow{\mu }=NIA\hat{n}$

From the data given in the question,

$\overrightarrow{\mu }=(100\times 0.5\times 0.08\times 0.04)\hat{i}=0.16\hat{i}{\text{Am}}^2$

Thus, torque acting on the coil is $\hat{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}=0.16\hat{i}\times \frac{0.05}{\sqrt{2}}\hat{j}=5.66\times {10}^{-3}\hat{k}\text{Nm}$

Hence, option (b) is the correct answer.