MHT CET · Physics · Magnetic Effects of Current
The magnetic field at the centre of a current carrying circular coil of an area ' \(A\) ' is ' \(B\) '. The magnetic moment of the coils is
[ \(\mu 0=\) permeability of free space.]
- A \(\frac{2 B A^{3 / 2}}{\mu_0 \pi^{1 / 2}}\)
- B \(\frac{B A^2}{\mu_0 \pi}\)
- C \(\frac{\mu_0 \pi^{1 / 2}}{B A^{3 / 2}}\)
- D \(\frac{B A^{3 / 2}}{\mu_0 \pi}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 B A^{3 / 2}}{\mu_0 \pi^{1 / 2}}\)
Step-by-step Solution
Detailed explanation
The correct option is (A)
\(\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}\)
Let \(r\) be the radius of the circular loop.
\(\therefore A=\pi r^2\) or \(r=\sqrt{\frac{A}{\pi}}\)
Magnetic field at the centre of the loop is
\(\begin{aligned} & B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 I}{2 \sqrt{\frac{A}{\pi}}} \\ & I=\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\end{aligned}\)
The magnetic moment of the loop is
\(M=I A=\left(\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\right) A=\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}\)
\(\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}\)
Let \(r\) be the radius of the circular loop.
\(\therefore A=\pi r^2\) or \(r=\sqrt{\frac{A}{\pi}}\)
Magnetic field at the centre of the loop is
\(\begin{aligned} & B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 I}{2 \sqrt{\frac{A}{\pi}}} \\ & I=\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\end{aligned}\)
The magnetic moment of the loop is
\(M=I A=\left(\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\right) A=\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}\)
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