Question

Due to the. Flow of current in a circular loop of radiius r the magnetic field produced at the centre of the loop is



b. The magnetic moment of the loop is

Answer 1

magnetic field due to circular loop and the magnetic moment due to loop and Bohr Magneton.

Answer 2

The magnetic field at center $B = \frac{\mu_0\times I}{2{R} }$

Step by step explanation:

According to Biot-savart law :

Magnetic field due to small element of current carrying wire is equal to

$db= \frac{\mu_0\times I(dl\times r)}{4\pi {r^3} }$

where I is the current in the direction of small element.

Making tangent at circle, the angle between tangent and center = 90°

and length of small arc = Rd∅

So

$db= \frac{\mu_0\times I(Rd\theta RSin90)}{4\pi {r^3} }$

On integrating the Biot sawart law from 0 to 2π

$B = \frac{\mu_0\times I(\theta )}{4\pi {R} }$

where $\theta$ limits from 0 to 2π

So,

$B = \frac{\mu_0\times I}{2{R} }$

$\textbf {\Large The magnetic field at center =}B = \frac{\mu_0\times I}{2{R} }$