00:01
So in this problem, we're looking at this grid here where we know we only have an electric field that goes along the y -axis.
00:10
So we only have to worry about a y component for the electric field.
00:15
And what we're looking for in the first two parts of this problem is whether the electric field is positive or negative and what the magnitude of this electric field is.
00:25
So one way that we can find the electric field from the electric potential is that if the potentials, is known as a function of the coordinates, so a coordinate system xyz, like we have here.
00:37
What we can do is the components of the electric field at any point are given by the partial derivatives of the potential.
00:47
So what does that mean if we write it down in a formula? so here i'll write it down for the y component, since that's the only one that we're looking at.
00:55
We would have the electric field along the y component.
00:59
It's going to be equal to negative, delta v over delta y so basically the change in v divided by the change in y over a certain line along along this axis or on this axis we take the negative of that and that's going to give us our electric field magnitude and whether it's positive or negative so if we go ahead and look between points a and b we know that the difference and the potential difference between point a and b is 12 volts.
01:35
So we can go ahead, put that up top here.
01:40
And we are given the distance of a and b from the origin.
01:45
A is 8 centimeters and b is 15 centimeters.
01:48
And to make sure that our units are consistent, we're just going to convert these to meters before we plug them in...