MHT CET · Physics · Magnetic Effects of Current

Two long conductors separated by a distance 'd' carry currents \(I_1\) and \(I_2\) in the same direction. They exert a force ' \(\mathrm{F}\) ' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance between them is also increased to \(3 \mathrm{~d}\). The new value of force between them is

A \(-2 \mathrm{~F}\)
B \(\frac{\mathrm{F}}{3}\)
C \(\frac{-2 \mathrm{~F}}{3}\)
D \(\frac{-\mathrm{F}}{3}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{-2 \mathrm{~F}}{3}\)

Step-by-step Solution

Detailed explanation

The force per unit length of the conductors is given as:
\(\mathrm{F}=\frac{\mu_4 \mathrm{I}_1 \mathrm{I}_2}{2 \pi \mathrm{d}}\)
When the value and direction of current in the first conductor and the distance between the conductors are changed,
\(\begin{aligned}
\therefore \quad \mathrm{F}_2 & =\frac{-\mu_0 2 \mathrm{I}_1 \mathrm{I}_2}{2 \pi \times 3 \mathrm{~d}} \\
\therefore \quad & \frac{\mathrm{F}_2}{\mathrm{~F}}=\frac{-2}{3} \\
\mathrm{~F}_2 & =-\frac{2 \mathrm{~F}}{3}
\end{aligned}\)

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