00:01
So we know that the magnetic field line, due to current flowing from the south to the north, is along concentric vertical lines downwards, downwards meaning into the paper and at eastward points, and then upwards, which essentially out of the paper, at westward points.
00:20
This is all clockwise with respect to an observer facing north end.
00:27
So given this we have that first, at any point below the current wire, the needle is going to experience two magnetic fields.
00:42
So we have, sorry, this little lower.
00:50
My apologies.
00:53
Here we have the northern direction and we have the western direction.
00:57
We have a vector here, b sub e.
01:00
This would be the magnetic field, b sub c, the magnetic field due to the current.
01:06
Carrying wire and then going up would be b sub e this would be the magnetic field due to the earth we have then a resultant magnetic field and we can actually let's draw dash lines to better represent this this would essentially be our vector our resultant's vector and so we can say that then an angle theta would be we can say tant of theta would be given by b sub c over b sub e and theta would equal arc tan of b sub c over b sub e.
02:05
So we can say that the compass needle placed essentially at a point below the current wire, we could say that then will be in a direction theta.
02:48
Of course, this would be west of north, where theta is equaling arc tan of the magnitude of the current carrying wire divided by the magnetic field of the earth.
03:10
We then have a needle above the current wire, and here we have the eastern direction, then the northern direction...