Question

Two long, parallel wires separated by 0.496 m carry equal currents of 11.062 A in the same direction. Find the magnitude of the net magnetic field 0.703 m away from each wire on the side opposite the other wire . Express your answer in microTesla.

Answer 1

In order to solve this exercise, let us first recap about point and cross notation. They are used to indicate vectors which are entering and leaving the screen. They are as follows:

You can think of it as an arrow. When the arrow is going away from us, we see the end of it, which is a cross. However, when it is coming in our direction, we see its tip, which is a point.

Now, starting into the problem, we can draw it as the following:

This happens as each wire with a flowing current generates a magnetic field that spins around it, as you can see in this drawing:

Now, we want to calculate the resulting magnetic field in the following point:

So, we can calculate our resulting magnetic field as:

`B=(\mu_0i)/(2\pi)((1)/(r_1)+(1)/(r_2))`

Which, replacing the values, gives us:

`B=(\mu_0*11.062)/(2\pi)*((1)/(0.703)+(1)/(0.703+0.496))=4.99\mu T`

Then, our final answer is B=4.99uT