A conductor with an inner cavity, like that shown in Fig. 22.23c, carries a total charge of +5.00 nC. The charge within the cavity, insulated from the conductor, is −6.00 nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?

Video transcript

Hey everyone. So this problem is dealing with electric point charges. Let's see what they're asking is we have a point charge of minus 10 nano columns located within a spherical metal shell That carries a total charge of nana problems. What is the net charge? This is a two part question of the internal part one and the external part two surfaces of the shell. So let's kind of draw what's going on here. So we have this metal shell, metal means we know that it's conducting and we have a point charge. That point charge has A charge of -10 Nano columns and then the total charge Is given to us as 30 nano problems. So we can recall that a Gaussian service within a conductor must enclose zero net charge And the electric field inside the conductor is zero. So If we have a charge inside the internal surface of -10 Nano columns, that means that the charge on the internal surface must be the opposite. And so that means that the Q internal is going to be the opposite of this point charge, which is positive 10 nana. Cool. Um, so the first part of this problem is really just a check to make sure that you understand the basics of Gaussian surfaces. So we look at our potential answers, we can see that off of that A and B are not correct. So let's look at Part two. The external service. So the for the external surface, the charge is a combination of the net charge on the conductor and the charge moved to the internal internal surface. So we can write that equation as our total charge is equal to the internal charge and the external charge We solve for the internal charge in part one, we were given the total charge in the problem. And so from here you can just rearrange this equation to show that the external charge is equal to the total charge minus the internal charge or 30 nano columns minus 10 nano columns, which equals positive nano columns. And so let's look at our potential answers. C. Is wrong. D. Is correct Where the internal charge is 10 Nana columns and the external charge is columns. That's all we have for this problem. We'll see you in the next video. Yeah.