Question

Two infinitely long straight wires having linear charge densities −λ and 3λ are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other.

Answer 1

Given: λ₁ = −λ

λ₂ = 3λ

The force per unit length between two infinitely long straight parallel wires with linear charge densities λ₁ and λ₂ is given by:

`f  = F/L= 1/(2piε_0) (λ_1 λ_2)/r`

= `1/(2piε_0) ((−λ)(3λ))/r`

= `1/(2piε_0) (-3λ^2)/r`

= `-(3λ^2)/(2piε_0r)`

Taking the absolute value for the magnitude:

= `(3λ^2)/(2piε_0r)`

Since the charges have opposite signs (λ₁ is negative and λ₂ is positive), the force is attractive.