Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be

Question

Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be (A) (B A2/μ0 π) (B) (B A3 / 2/μ0 π) (C) (B A3 / 2/μ0 π1 / 2) (D) (2 B A3 / 2/μ0 π1 / 2)

Tardigrade Admin · Accepted Answer

B=(μ0/4 π) (2 π i/r)=(μ0 i/2 r) or i=(2 B r/μ0) Also, A=π r2 or r=((A/π))1 / 2 Magnetic moment, M=i A=(2 B r/μ0) A =(2 B A/μ0) ×((A/π))1 / 2 =(2 B A3 / 2/μ0 π1 / 2)

Q. Magnetic field at the centre of a circular loop of area $A$ is $B$ . The magnetic moment of the loop will be

$\frac{B A ^{2}}{μ _{0} π}$

$\frac{B A ^{3/2}}{μ _{0} π}$

$\frac{B A ^{3/2}}{μ _{0} π ^{1/2}}$

$\frac{2 B A ^{3/2}}{μ _{0} π ^{1/2}}$

$B = \frac{μ _{0}}{4 π} \frac{2 πi}{r} = \frac{μ _{0} i}{2 r}$
or $i = \frac{2 B r}{μ _{0}}$
Also, $A = π r^{2}$ or $r = (\frac{A}{π})^{1/2}$
Magnetic moment, $M = i A = \frac{2 B r}{μ _{0}} A$
$= \frac{2 B A}{μ _{0}} \times (\frac{A}{π})^{1/2}$
$= \frac{2 B A ^{3/2}}{μ _{0} π ^{1/2}}$

Q. Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be

μ0​πBA2​

μ0​πBA3/2​

μ0​π1/2BA3/2​

μ0​π1/22BA3/2​