Question

Two power lines, each 290 m in length, run parallel to each other with a separation of 23 cm. If the lines carry parallel currents of 120 A, what are the magnitude and direction of the magnetic force each exerts on the other

Answer 1

To solve this problem we will apply the concepts related to the Magnetic Force, which is defined as the product between the currents multiplied by the length where they are transmitted and inversely proportional to the distance that separates them, considering between them, the costs indicated below . We will simply replace the values and obtain the desired value,

$F = \frac{\mu_0 I_1I_2 l }{2\pi d}$

Here,

$\mu_0$ = Permeability of free space

$I_{1,2}$ = Current at each state

$l$ = Length

$d$ = Distance of separation

Replacing with our values we have that the force is,

$F = \frac{(4\pi *10^{-7})(120)(120)(290)}{2\pi (0.23)}$

$F = 3.63N$

Therefore the magnitude of the force is 3.63N, and  if the currents are in same direction then force is attractive, while if the currents are in opposite direction then force is repulsive ( force is same).