Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. The surface charge density for each plate has magnitude 47.0 nC/m^2. (c) If the separation between the plates is doubled while the surface charge density is kept constant at the given value, what happens to the magnitude of the electric field and to the po­tential difference?

Video transcript

Welcome back everybody. We are taking a look at two equal giant sheets of metal placed across from one another. We are told that the distance between them is 54 mm and that they each have a charge density of 20.2 nano columns meter squared. Now we are told that the separation of the seats uh sorry of the sheets is going to be tripled. So the new distance will be three times the old distance. But we're told that the new charge density will be the same as the old charge density. And we are asked how this is going to affect both the magnitude of the electric field and the potential difference in the sheets. We have formula. So let's just look at our formulas here. We have that the magnitude of our electric field is equal to the charge density over our electric constant. We also know that our potential difference equal to the magnitude of the electric field times the distance. So let's go ahead and start out with our electric field. I'm going to sub in our new value of of sigma for our old value. So we will have sigma. Nu is divided by our electric constant. Well this of course is just equal to our old sigma divided by our electric constant which is equal to our old e. Meaning that our electric field will simply stay the same now, what about our potential. Well, our potential, our new potential will be equal to the magnitude of our electric field uh times our new distance. Our new distance is three times the old distance. This is equal to three times E. D. Which is three times the old potential, meaning that this will be tripled in the end. So we have found that our new electric field will be the same and that our new potential difference will be tripled corresponding to answer choice. A thank you all so much for watching. Hope this video helped. We will see you all in the next one.