# When Electric Field is 0 is potential also 0?

Alex Hughes
So here is how my book defined electric potential. If you take a charge, it will have a corresponding electric field associated with it. If you put another charge in that electric field, an electrostatic force will act on it and give it kinetic energy. This kinetic energy can't come from thin air, therefore it has to come from the electric potential energy stored in the charges. To account for electric potential energy, an electric potential is defined. The electric potential is simply the electric potential energy per charge. This made sense to me until I got to a part about conductors. They said the electric potential is constant all throughout the conductor, but inside the conductor the electric field is 0. This doesn't make sense to me. Don't you need an electric field in order for a force to act on a charge which would then give it an electric potential. Without any electric field, how could you possibly have an electric potential? I looked online and everybody said zero electric field just means that the CHANGE in potential will be 0, and possibly could mean the potential is 0 but its not certain. Can somebody please explain to me why this is. I'm really confused. Thanks.

What if the electric field at a point was a direction and the voltage gradient at that point, specified in volts per metre?

Mentor
If you put another charge in that electric field, an electrostatic force will act on it and give it kinetic energy.
More generally, the potential at a given location is the amount of work per unit charge that you will have to do to slowly move that charge from a defined reference point to the given location. If the given location is a region with no field then the charge can be moved freely anywhere within that region without any additional work. But if there is a field between the region and the reference point then it takes some work to go through that field. In fact, it takes the same amount of work to get anywhere within the region, but because of the intervening field that amount of work is non zero. Therefore, a zero field implies a constant voltage, not a zero voltage.

• Alex Hughes
Alex Hughes
More generally, the potential at a given location is the amount of work per unit charge that you will have to do to slowly move that charge from a defined reference point to the given location. If the given location is a region with no field then the charge can be moved freely anywhere within that region without any additional work. But if there is a field between the region and the reference point then it takes some work to go through that field. In fact, it takes the same amount of work to get anywhere within the region, but because of the intervening field that amount of work is non zero. Therefore, a zero field implies a constant voltage, not a zero voltage.
Thanks, that makes sense

Last edited:
• Dale