AP EAMCET · PHYSICS · Magnetic Effects of Current
If a wire of length ' \(L\) ' carrying a current ' \(i\) ' is bent in the shape of a semi-circular arc as shown in the figure, then the magnetic field at centre of the arc is
- A \(\frac{\pi \mu_{\mathrm{o}} \mathrm{i}}{4 \mathrm{~L}}\)
- B \(\frac{\pi \mu_{\mathrm{o}} \mathrm{i}}{2 \mathrm{~L}}\)
- C \(\frac{\mu_{\mathrm{o}} \mathrm{i}}{2 \pi \mathrm{~L}}\)
- D \(\frac{\mu_{\mathrm{o}} \mathrm{i}}{4 \pi \mathrm{~L}}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi \mu_{\mathrm{o}} \mathrm{i}}{4 \mathrm{~L}}\)
Step-by-step Solution
Detailed explanation
\(L = \pi R \Rightarrow R = \frac{L}{\pi}\) \(B = \frac{\mu_0 i}{4R} = \frac{\mu_0 i}{4(\frac{L}{\pi})} = \frac{\pi \mu_0 i}{4L}\)
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