TS EAMCET · Physics · Magnetic Effects of Current
A current ' \(i\) ' is flowing through a wire of length ' \(L\) '. If it is made into a circular loop of one turn, then its magnetic moment is
- A \(\frac{\mathrm{L}^2 \mathrm{i}}{4 \pi}\)
- B \(\frac{\mathrm{L}^2}{4 \pi}\)
- C \(\frac{4 \pi}{\mathrm{L}^2 \mathrm{i}}\)
- D \(4 \pi \mathrm{L}^2 \mathrm{i}\)
Answer & Solution
Correct Answer
(A) \(\frac{\mathrm{L}^2 \mathrm{i}}{4 \pi}\)
Step-by-step Solution
Detailed explanation
Length, \(L=2 \pi r \Rightarrow r=\frac{L}{2 \pi}\) Magnetic moment, \(\mathrm{M}=\mathrm{iA}=\mathrm{i} \pi\left(\frac{\mathrm{L}}{2 \pi}\right)^2\) \(=\mathrm{i} \times \pi \times \frac{\mathrm{L}^2}{4 \pi^2} \quad \therefore \mathrm{M}=\frac{\mathrm{IL}^2}{4 \pi}\)
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