Question

"two long parallel wires that are 0.30 m apart carry currents of 5.0 a and 8.0 a in the opposite direction. find the magnitude of the force per unit length that each wire exerts on the other wire and indicate if the force is attractive or repulsive. (μ0 = 4π × 10-7 t • m/a) "

Answer 1

The magnetic field B generated by wire 1 at distance r (where wire 2 is located) is
$B= \frac{\mu _0 I_1}{2 \pi r}$
where I1 is the current in wire 1. So, the force exerted on a segment $\Delta L$ of wire 2 is
$F=I_2 \Delta L B$
By susbstituting B inside the expression of F, we find the formula for the force per unit of length between the two wires:
$\frac{F}{\Delta L}=\mu_0 \frac{I_1 I_2}{2 \pi r}$
where r is the distance between the two wires.
By susbstituting the numbers of the problem, we get
$\frac{F}{\Delta L}=(4\pi \cdot 10^{-7} Tm/A ) \frac{(5.0 A)(8.0 A)}{2 \pi (0.30 m)}=2.7 \cdot 10^{-5}N$