COMEDK · Physics · 21. Magnetic Effects of Current
A current I flows in an infinitely long wire with cross section in the form of semi-circular ring of radius \(1 \mathrm{~m}\). The magnitude of the magnetic induction along its axis is
- A \(\dfrac{\mu_0 \mathrm{I}}{2 \pi} \mathrm{T}\)
- B \(\dfrac{\mu_0 \mathrm{I}}{2 \pi^2} \mathrm{~T}\)
- C \(\dfrac{\mu_0 \mathrm{I}}{\pi^2} \mathrm{~T}\)
- D \(\dfrac{\mu_0 \mathrm{I}}{4 \pi^2} \mathrm{~T}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{\mu_0 \mathrm{I}}{\pi^2} \mathrm{~T}\)
Step-by-step Solution
Detailed explanation
Current per unit angle: \(dI = \dfrac{I}{\pi}d\theta\) Magnetic field due to element (infinite wire) at axis (distance \(R\)): \(dB = \dfrac{\mu_0 dI}{2\pi R} = \dfrac{\mu_0 I}{2\pi^2 R}d\theta\) By symmetry, only sine components add up:…
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