Question

Two long parallel wires carry currents \(5A\) and \(2A\) and are separated by \(0.2m\). Find the force per unit length between them.

• A. \(5\times10^{-6}N/m\)
• B. \(2\times10^{-5}N/m\)
• C. \(1\times10^{-5}N/m\)
• D. \(1\times10^{-4}N/m\)

Hint:

The force per unit length between two parallel currents is directly proportional to the product of currents and inversely proportional to their separation.

Answer 1

The Correct Option is C

Using \[ \frac{F}{L} = \frac{\mu_0I_1I_2}{2\pi d} \] Substituting \[ I_1=5A,\quad I_2=2A,\quad d=0.2m \] \[ \frac{F}{L} = \frac{4\pi\times10^{-7}\times5\times2} {2\pi\times0.2} \] \[ = 10^{-5}N/m \] Final Answer: \[ \boxed{1\times10^{-5}N/m} \] Hence option \[ \boxed{(C)} \]