Question

Two straight wires located one-fifth of a meter from each other carry current in different directions. Current I1 = 13 A is into the page and I2 = 18 A is out of the page. Determine the magnitude and direction of the magnetic field for each of the wire and determine the magnitude of the magnetic field between the two wires.

Answer 1

The given situation can be illustrated as follow:

The red circles repersent the magnetic field produced by the currents on the wire.

As you can notice, between the wires the direction of the magnetic field is the same.

Consider that the magnetic field produced by a current I in a wire, at a distance r, is given by the following formula:

`B=(\mu_0I)/(2\pi r)`

where,

r: distance at the center betwen the wires = 0.20m/2 = 0.10m

μ0: permeability of free space = 4π*10^-7 Tm/A

Then, the total magnetic field between the wire is the sum of the magnetic fields generated by each wire:

`B=(\mu_0)/(2\pi(0.10m)^2)(I_1+I_2)=\frac{4\pi\cdot10^(-7)Tm\text{ /A}}{2\pi(0.10m)^2}(13A+18A)=6.2\cdot10^(-4)T`