COMEDK · Physics · 21. Magnetic Effects of Current

The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ratio of the magnetic field produced at the centre of the coil before the doubling of the radius to the magnetic field after doubling of the radius.

A 2 : 1
B 1 : 2
C 2 : 3
D 3 : 2

Verified Solution

Answer & Solution

Correct Answer

(A) 2 : 1

Step-by-step Solution

Detailed explanation

The magnetic field \(B\) at the centre of a circular coil of radius \(R\) carrying current \(I\) is given by the formula \(B = \dfrac{\mu_{0} I}{2R}\). Let the initial radius be \(R_{1} = R\) and the initial magnetic field be \(B_{1} = \dfrac{\mu_{0} I}{2R}\). After doubling 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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