ExamBro
ExamBro
MHT CET · Physics · Magnetic Effects of Current

Magnetic induction produced at the centre of a circular loop of radius ' R ' carrying a current is ' \(B\) '. The magnetic moment of the loop is ( \(\mu_0=\) permeability of free space)

  1. A \(\frac{\mathrm{BR}^3}{2 \pi \mu_0}\)
  2. B \(\frac{2 \pi \mathrm{BR}^3}{\mu_0}\)
  3. C \(\frac{\mathrm{BR}^2}{2 \pi \mu_0}\)
  4. D \(\frac{2 \pi \mathrm{BR}^2}{\dot{\mu}_0}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2 \pi \mathrm{BR}^3}{\mu_0}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{m}=\mathrm{nIA}\)
For coil, magnetic induction at the centre,
\(\begin{aligned}
& \quad B=\frac{\mu_0 n I}{2 R} \\
& \therefore \quad I=\frac{B \times 2 R}{\mu_0 n} \\
& \\
& \text { For } n=1, \text { Area } A=\pi R^2 \\
& \\
& m=\frac{B \times 2 R}{\mu_0} \times \pi R^2=\frac{2 \pi B R^3}{\mu_0}
\end{aligned}\)