Question

Current 'i' is carried in a wire of length L. If the wire is turned into circular coil, the maximum magnitude of torque in a given magnetic field B will be

• A. $\frac{L^2{B}^2}{2}$
• B. $\frac{L^{2}B}{2}$
• C. $\frac{L^{2}iB}{4\pi }$
• D. $\frac{L^{2}B}{4\pi }$

Answer 1

The correct option is C $\frac{L^{2}iB}{4\pi }$

The torque experienced by the wire in the magnetic field is:

${\tau }_{max}=NiAB=1\times i\times \left(\pi r^2\right)\times B(2\pi r=L,\Rightarrow r=\frac{L}{2\pi })$

${\tau }_{max}=\pi i{\left(\frac{L}{2\pi }\right)}^{2}B=\frac{L^{2}iB}{4\pi }$