00:01
Yeah, here we're going to take a quick look at an experiment that you could use to determine either the mass or a charge on a charged sphere.
00:12
And here it looks like the mass is unknown.
00:17
But what we're doing is placing the sphere between two parallel capacitor plates, two conducting plates.
00:24
A important thing to note is that the sphere should be small in relationship to the size of the plates, and you should try to maintain the sphere as close to the center as possible.
00:41
And the idea is that the capacitor plates will make a uniform electric field in the space between them.
00:49
But if you get too close to the edges, you could find up looking at fringing fields.
01:00
But anyway, you are placing the capacitor plates, you're connecting those to a variable voltage supply variable, and you are cranking up the voltage, and you are measuring the angle that the string, the sphere is hanging from, makes to the vertical.
01:23
So how would you measure that? oh, probably with a protractor.
01:27
So hang a protractor up close to the support point to measure the theta.
01:35
That doesn't look quite right, but you get the idea.
01:40
It may take a little bit of practice to get that protractor in the right place.
01:45
So you're going to measure the following quantities.
01:48
There is a spacing between the plates.
01:53
We'll call that s.
01:54
So we're going to measure s as carefully as possible using, say, calipers.
02:01
You're going to vary the voltage measure with the dvm, just to be sure.
02:22
Some power supplies have volt meters built in, but we'll just make sure that there is some way to measure that.
02:29
And the theta will be measured with a protractor.
02:36
And that will be your dependent variable, which will depend on the voltage that is chosen.
02:48
Let's see.
02:50
So some known quantities, we'll assume these are known.
02:58
Cube will come from a charge sensor.
03:02
We'll assume somebody has done that, and g will just take the be 9 .8 meters per second squared.
03:12
And the idea in the experiment is, as you crank the voltage up, the angle will change.
03:20
And the reason why is there is equilibrium between the tension in the string supporting the mass, the weight of the mass, m .g, and the electrical force.
03:40
I may not have that shown right, but what we basically have is the sum of the forces on the mass is equal to zero.
03:51
And so we can take a look at the sum of the x components and the sum of the y components.
04:01
And so we have the electrical force, which is along the positive x, we'll call positive y up, but the electrical force is pointing to the positive right, positive x, and that has got to be equal to 10.
04:27
Tension times sine of theta, looking at the little triangle that the tension makes.
04:36
The x component goes with the sign of that.
04:40
The sum of the y is mg, some of the y, minus mg, but we'll move it over, so it's positive.
04:51
But that has to be balanced by tension, cosine of theta.
04:56
And if we take the ratio between those two, so we want to divide the two equations by each other, and we get then that the lf electric over mg equals tangent theta, sine of theta over cosine theta, which is tangent of theta.
05:28
The electric force, we can expand that out a little bit, so here's some electricity relationships that will lead.
05:41
First of all, f -electric is equal to q times the electric field, and the electric field is the voltage difference between the plates v .e.
05:56
Divided by s...