Question

Two thin long parallel wires, \(W_1\) and \(W_2\) separated by distance '\(a\)', carry currents \(i\) and \(3i\) respectively in the same direction. The magnitude of the force per unit length exerted by wire \(W_1\) on wire \(W_2\) is

• A. \(\frac{μ_0\,i^2}{2π\,a}\)
• B. \(\frac{μ_0\,i^2}{π\,a}\)
• C. \(\frac{3μ_0\,i^2}{2π\,a}\)
• D. \(\frac{2μ_0\,i^2}{3π\,a}\)

Hint:

The force per length between parallel wires is mu0 i1 i2 / (2 pi a).

Answer 1

The Correct Option is C

Step 1: Field Method:
Wire $W_1$ (current $i$) produces a field $B=\dfrac{\mu_0i}{2\pi a}$ at the position of $W_2$.

Step 2: Force on W2:
Force per length on $W_2$ is $B\times(3i)=\dfrac{\mu_0i}{2\pi a}\times3i=\dfrac{3\mu_0i^2}{2\pi a}$.

Step 3: Answer:
Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C) } \frac{3\mu_0i^2}{2\pi a}} \]