Magnetic field at the centre of a circular lo | vedclass

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(B) Let $r$ be the radius of the circular loop. The area of the loop is $A = \pi r^{2}$.Therefore,$r = \sqrt{\frac{A}{\pi}}$.The magnetic field $B$ at

Vedclass · Accepted Answer

$\frac{2 B A^{\frac{3}{2}}}{\mu_{0} \pi^{\frac{1}{2}}}$

Vedclass · Answer

(B) Let $r$ be the radius of the circular loop. The area of the loop is $A = \pi r^{2}$.Therefore,$r = \sqrt{\frac{A}{\pi}}$.The magnetic field $B$ at the centre of the circular loop is given by $B = \frac{\mu_{0} I}{2 r}$.Substituting the value of $r$,we get $B = \frac{\mu_{0} I}{2 \sqrt{\frac{A}{\pi}}}$.Solving for current $I$,we get $I = \frac{2 B}{\mu_{0}} \sqrt{\frac{A}{\pi}}$.The magnetic moment $M$ is given by $M = I A$.Substituting the value of $I$,we get $M = \left( \frac{2 B}{\mu_{0}} \sqrt{\frac{A}{\pi}} \right) A$.$M = \frac{2 B}{\mu_{0}} \cdot \frac{A^{1/2}}{\pi^{1/2}} \cdot A = \frac{2 B A^{3/2}}{\mu_{0} \pi^{1/2}}$.

Magnetic field at the centre of a circular loop of area $A$ is $B$. The magnetic moment of the loop will be ($\mu_{0} =$ permeability of free space).

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