00:01
So the distance from the origin to a point on the line is going to be squared of, it's going to be 3 minus 0 squared, which 3 squared plus 4 minus 0 squared plus z prime minus 0 squared.
00:17
It's going to be the square root of 9 plus 16, so it's 25 plus z prime squared.
00:26
The infinitesimal contribution to the electric field at the origin, d .e is going to be 1 over 4 pi epsilon not times row l, d, l over r squared, r unit vector.
00:46
And now the r unit vector is going to be r divided by its magnitude.
00:54
It's going to be 3, 4, z prime divided by square root 25 plus z prime.
01:03
And so because of that, we have an x component.
01:06
Component to be 1 over 4 pi epsilon not charge density dl divided by 25 plus z prime squared so three halves times three in the x direction that's going to be the same in the y and d direction sorry in z direction except that we have different set of three we here have 4 for y and z prime for z so the total electric field we have to take the integrals so for x it's going to be 3 row l for pi epsilon not integral from minus infinity to infinity of these z prime divided by 25 plus z prime squared to the 3 over 2 b3.
02:48
Now, the standard result from minus infinity of dz prime over a squared plus z squared, or z prime squared to three halves, is 2 over a squared.
03:06
And now a is 5...