### Video Transcript

A sphere has a surface uniformly charged with 1.00 coulombs. At what distance from its centre is the potential 5.00 megavolts?

We can call the given charge spread over the sphere 1.00 coulombs π. And the potential of 5.00 megavolts, weβll call π. We want to solve for the distance from the centre of the sphere, at which its potential is equal to π. Weβll call that distance π. Letβs start with a sketch of the sphere.

We have a sphere with charge π spread evenly over its surface. We donβt know the sphereβs radius. But we do know that at some point external to the sphere, at distance π from its centre, the potential is π, given as 5.00 megavolts.

To solve for that distance π, we can consider the mathematical relationship for the electric potential outside of a uniformly charged sphere. That potential π is equal to the charge π spread over the surface of the sphere divided by four ππ nought, where π nought is the permittivity of free space times the distance from the centre of the sphere π.

For our purposes, weβll treat π nought as having an exact value of 8.85 times 10 to the negative 12th farads per metre. So the electric potential π at distance π away from the centre of the sphere equals the charge spread over the sphere over four ππ nought π.

Rearranging this equation to solve for π, we find itβs π over four ππ nought π. For each of these three variables, we have values. So weβre now ready to plug in and solve for π. When we do, weβre careful to use units of volts in our expression for the potential difference.

Entering these values on our calculator, we find that to three significant figures π is 1.80 kilometres. Thatβs the distance from the centre of the sphere, at which π equals 5.00 megavolts.