Question

A current carring wire is bent to from a circuital coil. If this coil is placed in any other magnetic filed the maximum torque on the coil, the number of turns will be

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

Answer: (C)

4

$\text{Solution}:$

Let r be the radius of the coil and n be the number of turns formed.

L = $2\pi rn$ or

$r=\frac{L}{2\pi n}$

Maximum torque,

${\tau }_{max}=BnIA=BnI\pi r^2$

$=BnI\pi \times \frac{L^2}{4{\pi }^2{n}^2}=\frac{BI{L}^2}{4\pi n}$

Torque will be maximum if n = 1

$\therefore {\tau }_{max}=\frac{BI{L}^2}{4\pi }$

$\text{Hence A is the correct option}$