WBJEE · Physics · Electromagnetic Induction
A small bar magnet of dipole moment \(M\) is moving with speed \(v\) along \(x\) direction towards a small closed circular conducting loop of radius ' \(a\) ' with its centre \(O\) at \(x=0\) (see figure). Assume \(x>>a\) and the coil has a resistance \(R\). Then which of the following statemenmt(s) is/are true?
- A Magnetic field at the centre \(\mathrm{O}\) of the circular coil due to the bar magnet is \(\frac{\mathrm{M}}{\mathrm{x}^{3}}\)
- B Induced EMF is proportional to \(\frac{1}{x^{4}}\)
- C The magnetic moment \(\mu\) due to induced current in the coil is proportional to \(\mathrm{a}^{4}\)
- D The heat produced is proportional to \(\frac{1}{x^{6}}\)
Answer & Solution
Correct Answer
(C) The magnetic moment \(\mu\) due to induced current in the coil is proportional to \(\mathrm{a}^{4}\)
Step-by-step Solution
Detailed explanation
Magnetic field at an axial point is \(2\left(\frac{\mu_{0}}{4 \pi}\right) \frac{M}{x^{3}}\) \[ \phi=2\left(\frac{\mu_{0}}{4 \pi}\right) \frac{M}{x^{3}} \cdot \pi a^{2} \]…
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