Question

Two long straight wires are parallel to each other and are separated by 78 mm. The current in wire 1 is 3.55 A and the current in wire 2 is 2.75 A. What is the force per unit length between the two wires?

Answer 1

Answer:

$2.5\cdot 10^{-5}N$

Explanation:

The force per unit length between two current-carrying wires is given by:

$\frac{F}{L}=\frac{\mu_0 I_1 I_2}{2\pi r}$

where

$\mu_0$ is the vacuum permeability

$I_1, I_2$ are the two currents

r is the separation between the wires

In this problem, we have

$I_1 =3.55 A$ is the current in the first wire

$I_2 = 2.75 A$ is the current in the second wire

$r=78 mm=0.078 m$ is the separation between the wires

Substituting into the equation, we find

$\frac{F}{L}=\frac{(4\pi \cdot 10^{-7} H/m)(3.55 A)(2.75 A)}{2\pi (0.078 m)}=2.5\cdot 10^{-5}N$