MHT CET · Physics · Magnetic Effects of Current

\(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance \(A B\) and \(B C\) is same as ' \(d\) '. If ' \(F_1\) ' is the force exerted by \(\mathrm{B}\) on \(\mathrm{A}\) and \(\mathrm{F}_2\) is the force exerted by \(\mathrm{C}\) on \(\mathrm{A}\), then

A \(\mathrm{F}_1=\mathrm{F}_2\)
B \(\mathrm{F}_1=-\mathrm{F}_2\)
C \(\mathrm{F}_1=2 \mathrm{~F}_2\)
D \(\mathrm{F}_1=\frac{1}{2} \mathrm{~F}_2\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{F}_1=-\mathrm{F}_2\)

Step-by-step Solution

Detailed explanation

Force per unit length exerted by \(\mathrm{B}\) on \(\mathrm{A}\), \(\mathrm{F}_1=\frac{\mu_0(\mathrm{I})(\mathrm{I})}{2 \pi \mathrm{d}}=\frac{\mu_0 \mathrm{I}^2}{2 \pi \mathrm{d}}\) (outside the plane of paper) Force per unit length exerted by \(\mathrm{C}\) on \(\mathrm{A}\), \(\mathrm{F}_2=\frac{\mu_0(\mathrm{I})(2 \mathrm{I})}{2 \pi(2 \mathrm{~d})}=\frac{\mu_0 \mathrm{I}^2}{2 \pi \mathrm{d}}\) (Inside the plane of paper) \(\therefore \quad F_1=-F_2\)

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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