Question

Two long, parallel wires separated by 2.10 cm carry currents in opposite directions. The current in one wire is 1.40 A, and the current in the other is 3.30 A.

(a) Find the magnitude of the force per unit length that one wire exerts on the other. N/m
(b) Is the force attractive or repulsive? attractive repulsive Need Help?

Answer 1

Explanation:

Current in wire one, $I_1=1.4\ A$

Current in wire 2, $I_2=3.3\ A$

Separation between two parallel wires, d = 2.1 cm

(A) We need to find the magnitude of the force per unit length that one wire exerts on the other. It is given by the formula as follows :

$\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi d}\\\\\dfrac{F}{l}=\dfrac{4\pi \times 10^{-7}\times 1.4\times 3.3}{2\pi \times 2.1\times 10^{-2}}\\\\\dfrac{F}{l}=4.4\times 10^{-5}\ N/m$

So, the force per unit length that one wire exerts on the other is $4.4\times 10^{-5}\ N/m$.

(B) If the current is acting in opposite direction, then te force between them is repulsive.