Question

A wire of length l is bent in the form of a circular loop and is suspended in a region of a uniform magnetic field . When a steady current I is passed through the loop, the maximum torque experienced by it is

• A. $\frac{I{l}^{2}B}{4{\pi }^2}$
• B. $\frac{BI{l}^2}{4\pi }$
• C. $4{\pi }^{2}I{l}^{2}B$
• D. $\frac{I}{4\pi B{l}^2}$

Answer 1

The correct option is B

$\frac{BI{l}^2}{4\pi }$

The torque experienced by the loop $\tau =BIAsin\theta$. The maximum torque experienced ${\tau }_{max}=BIA$

Length of the loop $l=2\pi R\Rightarrow R=l/2\pi$

Area of the loop $A=\pi R^2=\frac{\pi l^2}{4{\pi }^2}=\frac{l^2}{4\pi }$

Torque,${\tau }_{max}=\frac{BI{l}^2}{4\pi }$