MHT CET · Physics · Magnetic Effects of Current

Two identical long parallel wires carry currents \(I_1\) and \(I_2\) such that \(I_1>I_2\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(6 \times 10^{-6} \mathrm{~T}\). If the direction of \(I_2\) is reversed, the field becomes \(3 \times 10^{-5} \mathrm{~T}\). The ratio \(\left(\frac{I_1}{I_2}\right)\) is-

A \(\frac{3}{4}\)
B \(\frac{1}{2}\)
C \(\frac{2}{3}\)
D \(\frac{3}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

Using ampere's law: \(B \propto I\) and \(B \propto 1 / d\).
For two wires separated by a distance \(d\), if \(B_1\) is the field when the currents are in the same direction and \(B_2\) is the field when currents are in opposite directions, then
\(\frac{B_1}{B_2}=\frac{\frac{\mu_0}{2 \pi}\left(\frac{i_1}{d}-\frac{i_2}{d}\right)}{\frac{\mu_0}{2 \pi}\left(\frac{i_1}{d}+\frac{i_2}{d}\right)}=\frac{1}{5}\)
On solving:
\(\begin{aligned} & \frac{\left(\frac{i_1}{i_2}-1\right)}{\left(\frac{i_1}{i_2}+1\right)}=\frac{1}{5} \\ & \therefore \frac{i_1}{i_2}=\frac{3}{2}\end{aligned}\)

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app