00:01
In this problem on magnetic forces and magnetic fields, we are told that four long parallel power lines each carry the same current of magnitude 100 ampiers, and the cross -sectional diagram represents a square with a side length of 20 centimeters.
00:21
We want to find the magnetic field at the center of the square for three different arrangements.
00:27
Now firstly, let's look at part c of the problem.
00:30
So in part c, we can label the currents as in the diagram, a, b, c, and d.
00:37
The magnetic field due to c and b are additive, as well as the magnetic fields due to a and d.
00:47
And so this tells us that the irresultant magnetic field is to the left, and the angles are about 45 degrees.
01:02
So we can then find this result in magnetic field at the center of the square b and b is b a cost 45 degrees plus b b cost 45 degrees plus magnetic field due to c b c times cost 45 degrees plus b d cost 45 degrees plus bd cost 45 degrees but these magnetic field strengths are all the same since the currents are the same.
01:46
So we can write this as 4 times b a times the cosine of 45 degrees.
01:55
And we can write this as 4 and you can expand the magnetic field since this is a long straight current current carrying conductor as mu not i over 2 pi r...