Question

Two long, parallel wires are attracted to each other by a force per unit length of 305 µN/m. One wire carries a current of 25.0 A to the right and is located along the line y = 0.470 m. The second wire lies along the x axis. Determine the value of y for the line in the plane of the two wires along which the total magnetic field is zero.

Answer 1

To solve this problem we will use the concepts related to the electromagnetic force related to the bases founded by Coulumb, the mathematical expression is the following as a function of force per unit area:

$\frac{F}{L} = \frac{kl_1l_2}{d}$

Here,

F = Force

L = Length

k = Coulomb constant

I =Each current

d = Distance

Force of the wire one which is located along the line y to 0.47m is $305*10^{-6}N/m$ then we have

$l_2 = \frac{F}{L} (\frac{d}{kl_1})$

$l_2 = (305*10^{-6}N/m)(\frac{0.470m}{(2*10^{-7})(25A))})$

$l_2 = 28.67A$

Considering the B is zero at

$y = y_1$

$\frac{kI_2}{2\pi y} =\frac{kI_1}{2\pi y_1}$

$\frac{(4\pi*10^{-7})(28.67)}{2\pi (y_1)} = \frac{(4\pi *10^{-7})(25)}{2\pi (0.47-y_1)}$

$y_1 = 0.25m$

Therefore the value of y for the line in the plane of the two wires along which the total B is zero is 0.25m