COMEDK · Physics · 21. Magnetic Effects of Current

Two similar coils \(A\) and \(B\) of radius '\(r\)' and number of turns '\(N\)' each are placed concentrically with their planes perpendicular to each other. If I and \(2 \mathrm{I}\) are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be:

A \(3 \mu_0 \dfrac{\mathrm{NI}}{\mathrm{r}}\)
B \(\sqrt{5}\left(\mu_0 \dfrac{\mathrm{NI}}{2 \mathrm{r}}\right)\)
C \(\sqrt{3}\left(\mu_0 \dfrac{\mathrm{NI}}{2 \mathrm{r}}\right)\)
D \(5 \mu_0 \dfrac{\mathrm{NI}}{2 \mathrm{r}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{5}\left(\mu_0 \dfrac{\mathrm{NI}}{2 \mathrm{r}}\right)\)

Step-by-step Solution

Detailed explanation

The magnetic field at the center of a circular coil of radius \(r\) with \(N\) turns carrying current \(I\) is given by \(B = \dfrac{\mu_0 NI}{2r}\). For coil \(A\) with current \(I\), the magnetic field is \(B_A = \dfrac{\mu_0 NI}{2r}\). For coil \(B\) with current \(2I\), the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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