Question

Two power lines run parallel for a distance of 254 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 140 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other.

Answer 1

To solve this problem we will apply the concepts related to the electromagnetic force given between two cables. For this purpose we will consider the following mathematical relation,

$F = \frac{\mu_0I_1I_2L}{(2\pi d)}$

Here,

$\mu_0$ = Permeability at free space

$I_{1,2}$ = Current

L = Length

d = Distance between them

With our values we have,

$F = \frac{(4\pi*10^{-7}) (140)(140) (254)}{(2\pi (40*10^{-2}))}$

$F = 2.4892N$

Therefore the force between the wires is 2.4892 N as the current flows in oposite direction, the force is away from each other.