Electric Potential Difference from a Point Charge

Good morning. In a previous lesson, we discussed how the electric potential from a point charge equals the kulum constant times the charge of the point charge divided by the distance from the point charge to the location of the electric potential. Today we're going to discuss the electric potential difference between two locations in the electric field of the point charge. — Flipics. [singing] It should come as no surprise to you that the electric potential difference between two locations in the electric field of a point charge equals the electric potential final minus the electric potential initial. In other words, all we need to do is substitute in the equation for electric potential final and electric potential initial. That's it. That seems pretty simple. Yep. — Yeah, sure. But I want to make sure you

understand what all this means. So, let's start with a positive point charge. We know the electric field which surrounds a positive point charge looks like this. To talk about the electric potential difference between two locations in the electric field of the positive point charge, let's add point A and point B to our illustration. Bobby, is the electric potential difference from point A to point B in our illustration a positive or a negative value? In other words, if a positive charge were to move from point A to point B, would it experience an increase or a decrease in electric potential energy? Okay. Uh we know that locations close to a positive point charge have a larger positive electric potential and locations farther from a positive point charge have a smaller positive electric potential. We know this because electric field lines point in the direction of decreasing electric potential. Just like gravitational field lines point down near the surf surface of the earth and gravitational potential decreases as the location of the gravitational potential moves down in the direction of the gravitational field. That means the electric potential at point B is larger than A. So going from point A to point B represents an increase in electric potential. So the electric potential difference from point A to point B is positive. You could also look at it in terms of math. The electric potential difference from A to B equals the kum constant time the charge over the distance for B minus A. You can factor out the kum constant time the charge and both of those are positive values. Parenthetically, we have the inverse of the distance from the point charge to point B minus A. You could see from the illustration that the distance to point B is smaller than A. That means the inverse of the distance to point B is larger than A. That means the parenthetical quantity is greater than zero. And the electric potential difference when moving from point A to point B is positive. — Actually, you can also look at it in terms of work. A positive test charge placed at point A would experience an electrostatic force away from the positive charge creating the electric field. That means it would take an external force to move a positive test charge closer to the central positive charge creating the electric field. Work done by that force would add electric potential energy to the system. That means the electric potential energy of the system would increase when moving a positive test charge toward the positive charge creating the electric field. Therefore, the electric potential increases when moving closer to the positive charge creating the electric field. And the electric potential difference from point A to point B would be positive. Well done. Those are all correct. Realize that all of your arguments are reversed when finding the electric potential difference from point B to point A. In other words, A is negative. — Hold up. — Yes, Bo.

— Does the path from point A to point B affect the electric potential difference? — Oh, that is a good question. Yeah. Okay, that is fair. Bo, your question essentially is, is the electric potential difference from point A to point B the same if we follow path one and two? Correct? — Yeah. — Okay. Remember the electrostatic force is a conservative force. That means the work done on the system by the electrostatic force is independent of path taken by the object. That means the change in electric potential energy of the system is independent of the path taken by the object. Therefore, the electric potential difference is also independent of the path. So no, the path from point A to point B does not affect the electric potential difference. Another way to look at it is in terms of the aqua potential surfaces which surround the positive charge creating the electric field. Remember those look like circles on the screen. However, they are spherical surfaces which are concentric with the charge creating the electric field. Each of those equipotential surfaces has the same electric potential. That is what equipotential means. In other words, as long as point A is on the equipotential surface with a radius of R sub A and point B subB, then the electric potential difference will be the same no matter what path is taken between those two equipotential surfaces. In other words, the electric potential difference between any point on the equipotential surface of radius R sub A and subb will have the same electric potential difference. And it does not matter what the path is between the two equipotential surfaces. — Wow. — Wa. — Yeah, — Billy. I could not have said it better myself and I will not try to. Thank you very much for learning with me today. I enjoy learning with you.