MHT CET · Physics · Magnetic Effects of Current

A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is

A $\frac{2}{π}$
B $\frac{π}{2}$
C $π$
D $\frac{4}{π}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{4}{π}$

Step-by-step Solution

Detailed explanation

Let

l

bet he length of metal wire.
When wire is bent into a circular coil of radius r, then

r = \frac{l}{2 π}

∴ A r e a, A = π {(\frac{l}{2 π})}^{2} = π \frac{l^{2}}{4 π^{2}}

∴

Magnetic dipole moment associated with circular coil,

μ_{c} = i A = i π (\frac{l^{2}}{4 π^{2}})

μ_{c} = \frac{i l^{2}}{4 π}

… (i)
When metal wire is bent into a square coil then side of square

a = \frac{l}{4}

∴ A r e a, A = a^{2} = \frac{l^{2}}{16}

∴

Magnetic dipole moment associated with square coil,

μ_{s} = i A = i \frac{l^{2}}{16}

∴ \frac{μ_{c}}{μ_{s}} = \frac{\frac{i l^{2}}{4 π}}{\frac{i l^{2}}{16}} = \frac{16}{4 π} = \frac{4}{π}

Hence, the ratio of magnetic dipole moment of circular and square coil is

4 : π

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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