Two long straight parallel wires are carrying charges $λ_1$ and $λ_2$ per unit length, respectively. The separation between their axes is $d$. The magnitude of the force exerted on unit length of one wire due to the charge on the other wire is

$f =\frac{λ_1λ_2}{2πε_0d}$

The correct answer is Option (1) → $f =\frac{λ_1λ_2}{2πε_0d}$

For a long straight charged wire, the electric field at distance $r$ from it is

$E = \frac{1}{2 \pi \epsilon_0} \cdot \frac{\lambda}{r}$

The force per unit length on the second wire due to the field of the first wire is

$\frac{F}{L} = \lambda_2 \, E_1 = \lambda_2 \cdot \frac{1}{2 \pi \epsilon_0} \cdot \frac{\lambda_1}{d}$

$\frac{F}{L} = \frac{\lambda_1 \lambda_2}{2 \pi \epsilon_0 d}$

Answer: $\; \frac{F}{L} = \frac{\lambda_1 \lambda_2}{2 \pi \epsilon_0 d}$