A straight wire carrying current \(i\) is turned into a circular loop. If the magnitude of magnetic moment…
A straight wire carrying current \(i\) is turned into a circular loop. If the magnitude of magnetic moment associated with it in MKS units is \(M\), the length of wire will be
\(4 \pi i M\)
\(\sqrt{\frac{4 \pi M}{i}}\)
\(\sqrt{\frac{4 \pi i}{M}}\)
\(\frac{M \pi}{4 i}\)
Solution
Suppose, \(l\) be the length of wire.
Hence, \(\quad l=2 \pi r \Rightarrow r=\frac{l}{2 \pi}\)
\(\therefore\) Magnetic dipole moment,
\(\begin{aligned}
M & =i A \\
M & =i \cdot \pi r^2 \Rightarrow=i \pi \cdot\left(\frac{l}{2 \pi}\right)^2=i \pi \cdot \frac{l^2}{4 \pi^2} \\
\Rightarrow M & =\frac{i l^2}{4 \pi} \\
l^2 & =\frac{4 M \pi}{i} \Rightarrow l=\sqrt{\frac{4 \pi M}{i}}
\end{aligned}\)