MHT CET · Physics · Magnetic Effects of Current
A circular current carrying coil has radius \(\mathrm{R}\). At what distance from the centre of the coil on the axis, the magnetic induction will become \(\frac{1}{8}\) th of its value at the centre of the coil?
- A \(\frac{2 \mathrm{R}}{\sqrt{3}}\)
- B \(\mathrm{R} \sqrt{3}\)
- C \(\frac{\mathrm{R}}{2 \sqrt{3}}\)
- D \(\frac{\mathrm{R}}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{R} \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(B_{axis} = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}\), \(B_{center} = \frac{\mu_0 I}{2R}\) \(\frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} = \frac{1}{8} \frac{\mu_0 I}{2R}\)
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