Magnetic induction at the centre of a circular loop carrying a current is B . If A is the area of the coil, the magnetic dipole moment of the loop is

Question

Magnetic induction at the centre of a circular loop carrying a current is B . If A is the area of the coil, the magnetic dipole moment of the loop is (A) (B A2/μ 0 π ) (B) (B A √A/μ 0) (C) (B A √A/μ 0 π ) (D) (2 B A/μ 0) √(A/π )

Tardigrade Admin · Accepted Answer

B =(μ0 i/2 r), A=π r2, r=√(A/π) m =i A=(B × 2 r/μo) × π r2 =(2 B/μo) π r3 =(2 B π/μo)((A/π))(3/2) =(2 B A/μo) √(A/π)

Q. Magnetic induction at the centre of a circular loop carrying a current is $B$ . If $A$ is the area of the coil, the magnetic dipole moment of the loop is

$\frac{B A ^{2}}{μ _{0} π}$

$\frac{B A A}{μ _{0}}$

$\frac{B A A}{μ _{0} π}$

$\frac{2 B A}{μ _{0}} \frac{A}{π}$

$B = \frac{μ _{0} i}{2 r}, A = π r^{2}, r = \frac{A}{π}$
$m = i A = \frac{B \times 2 r}{μ _{o}} \times π r^{2}$
$= \frac{2 B}{μ _{o}} π r^{3}$
$= \frac{2 B π}{μ _{o}} (\frac{A}{π})^{\frac{3}{2}}$
$= \frac{2 B A}{μ _{o}} \frac{A}{π}$

Q. Magnetic induction at the centre of a circular loop carrying a current is B . If A is the area of the coil, the magnetic dipole moment of the loop is

μ0​πBA2​

μ0​BAA​​

μ0​πBAA​​

μ0​2BA​πA​​