00:01
For this problem on the topic of electric fields, we are told that a thin wire has a length of 22 .13 centimeters and a uniform charge distribution of 5 .6 .35 times 10 to the minus 8 kooloms per meter.
00:12
The wire is shaped into a semicircle, centered at the origin, with a radius of l over pi, and we want to find the magnitude of the electric field at the center of the semicircle.
00:25
Now, the magnitude of the electric field at the center, due to a differential element dl, is de and de is equal to the electric constant k times the charge per unit length lambda times the length element dl over r squared.
00:47
The x components add to zero, leaving only a field in the y direction.
00:53
And so the y component d ey is equal to k lambda dl over over r squared sine theta.
01:08
Now, if we take the l to be r d theta, we have this to be k lambda r over r squared times sine theta d theta.
01:25
And so this becomes k times lambda over r times sine theta d theta.
01:35
We can integrate this from 0...