Question

Two long, straight wires are parallel and 16 cm apart. One carries a current of 2.9 A, the other a current of 5.7 A. (a) If the two currents flow in opposite directions, what is the magnitude (in N/m) and direction of the force per unit length of one wire on the other?

Answer 1

Explanation:

Given that,

Distance between two long wires, d = 16 cm = 0.16 m

Current in one wire, $I_1=2.9\ A$

Current in wire 2, $I_2=5.7\ A$    

The magnetic force per unit length of one wire on the other is given by the following expression as :

$\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi d}$

$\dfrac{F}{l}=\dfrac{4\pi \times 10^{-7}\times 2.9\times 5.7}{2\pi \times 0.16}$

$\dfrac{F}{l}=2.06\times 10^{-5}\ N/m$

The current is flowing in opposite direction, the magnetic force acting on it is repulsive. Hence, this is the required solution.