A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is 10.0 pC. The inner cylinder has radius 0.50 mm, the outer one has radius 5.00 mm, and the length of each cylinder is 18.0 cm. (a) What is the capacitance? (b) What applied potential difference is necessary to produce these charges on the cylinders?

Video transcript

Welcome back everybody. We are taking a look at a cylinder shaped capacitor. I'm just going to draw a kind of the front point of view here. So we can kind of imagine what this looks like on the inside here, we're going to have a copper cylinder and we are told that the radius of that inner copper cylinder is three centimeters or point oh three m on the outside. We are going to have that copper cylindrical shell in. We were told that the radius of the outside is four centimeters or point oh four m. Now, each cylinder has the same length of 10 centimeters or 100.1 m and we are told that it is charged with PICO. Cool. Um we are tasked with finding two things here. One, what is the capacitance of this capacitor and B. What is the potential difference across the capacitor here? So let's go ahead and start with part A. Here, luckily for a cylindrical concentric capacitor like this, we actually have a formula for this. It's simply two pi epsilon, naught times the length. All divided by the natural log of the radius of the outside, divided by the radius of the inside. So let's just go ahead and plug in all our values here, we have two pi times epsilon not of 8.85 times 10 to the negative 12. That's just a constant Times are length of .1. All divided by the natural log of . divided by .03. When you plug this into your calculator, we get a capacity of 1.93 times 10 to the negative 11th. Fair ads. Great. Now moving on to part B here, what is the potential difference across this capacitor here? Well, simply it's going to be the charge divided by the capacitance. So this is going to be five times 10 to the negative 11th, which that's just converting PICO columns, two columns divided by 1.93 times 10 to the negative 11th, which is our capacitance here. This is going to be equal to 2. volts. So now we have found both the potential difference and the capacitance and this of course, corresponds to our answer choice of a Thank you all so much for watching. Hope this video helped. We will see you all in the next one.