Question

The wire of length $l$ is bent into a circular loop of a single turn and is suspended in a magnetic field of induction $B$. When a current $I$ is passed through the loop, the maximum torque experienced by it is

• A. $\binom{\frac{1}{4\pi}}{ }BIl^{2}$
• B. $\frac{1}{4\pi}BI^{2}l$
• C. $\binom{\frac{1}{4\pi}}{ }BIl$
• D. $\binom{\frac{1}{4\pi}}{ }B^{2}Il$
• E. $\binom{\frac{1}{4\pi}}{ }B^{2}I^{2}l^{2}$

Answer 1

Answer: (A)

When the wire of length $l$ is bent into circular loop of radius $R$
$I=2 \pi r \Rightarrow r=\frac{l}{2 \pi}$
When current $I$ is passed through the loop, the torque acting on the loop.
$\tau =n \mid A B $
$\tau =I \times B \times \pi r^{2}$
$=I B \pi\left(\frac{l}{2 \pi}\right)^{2}=I B \frac{l^{2}}{4 \pi}=\left(\frac{1}{4 \pi}\right) B I l^{2}$