00:02
Alright, so in this problem we have the setup.
00:09
So we have a charged bar over here with lens a and total charge is q.
00:16
And we have a point charge negative q over here.
00:20
So q is positive and negative q is negative.
00:25
So for part a, we want to find out the electric field induced by the charge bar along the x -axis.
00:35
So to do that, we need to utilize the...
00:41
We just need to look at the very small part on the charge bar.
00:45
So we'll just look at this part, okay? the lens of this part is d -y.
00:50
So by using the columns law, we know that d -e -y, d -e is the electric field on the x -axis induced by this small part, equal 1 over 4 pi epsilon times, dq over r squared, right? so dq is the charge for the small part, and r is the distance from the small part to this location.
01:19
So we have this equal to 1 over 4 pi epsilon knot.
01:23
Dq, in this case, equal to lambda times dy.
01:28
And r squared is x squared plus y squared.
01:32
So x, this is x.
01:35
And y is the position of this d and lambda is the charge density of the charge bar, which is q over a.
01:46
So we have turned this equal to 1 over 4 pi epsilon, q over a times dy over x squared plus y squared.
01:57
So this is the electric field induced by the small part.
02:02
And the direction of this electric field is pointing to this direction.
02:07
I'm sorry, i mean the electric field is pointed to this direction.
02:12
To this direction.
02:14
E.
02:15
This is a de, okay.
02:17
And then we can look at the x component, the y component of this de.
02:23
So let's say the x component is d -e equals d -e times.
02:28
So remember that this is the chart bar and this is the interested point.
02:35
And this is the d -y.
02:37
So this is x.
02:39
This is the y.
02:41
So d -x will be equal to d -e times x over square root.
02:45
X squared plus y squared, right? and the de x, i'm sorry, d y equal to d e times y over square root x squared plus y squared.
03:02
So just plug the expression for d e into this two expressions, we can obtain the expression for d x and d y.
03:12
So d x is 1 over 4 pi absalom times q over a times y, sorry, no y, times x, d, y, times x, d, y over x squared plus y squared with power 3 over 2.
03:45
Okay.
03:46
And for this one, this equal 1 over 4 pi epsilon knot, q over a times a, d y, over x squared plus y squared, with power 3 over 2.
04:00
And then we can start doing integral to find out ex and ey.
04:07
So ex is d -e -x, which is so the integrating range is from 0 to a.
04:17
So it's 1 over 4 pi, absolute q over a.
04:23
Let's see, this is x, d -y, divide by, sorry, not squared...
