Magnetic induction produced at the centre of a circular loop of radius ' R ' carrying a current is ' $B$ '.…

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. $\frac{\mathrm{BR}^3}{2 \pi \mu_0}$
  2. $\frac{2 \pi \mathrm{BR}^3}{\mu_0}$
  3. $\frac{\mathrm{BR}^2}{2 \pi \mu_0}$
  4. $\frac{2 \pi \mathrm{BR}^2}{\dot{\mu}_0}$

Solution

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

Asked in: MHT CET 2024 (15 May Shift 1)

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