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# Electric Potential for AP Physics B & C

based on 2 ratings
By McGraw-Hill Professional
Updated on Feb 12, 2011

Practice problems for these concepts can be found at:

Electrostatics Practice Problems for AP Physics B & C

When you hold an object up over your head, that object has gravitational potential energy. If you were to let it go, it would fall to the ground.

Similarly, a charged particle in an electric field can have electrical potential energy. For example, if you held a proton in your right hand and an electron in your left hand, those two particles would want to get to each other. Keeping them apart is like holding that object over your head; once you let the particles go, they'll travel toward each other just like the object would fall to the ground.

In addition to talking about electrical potential energy, we also talk about a concept called electric potential.

Electric potential is a scalar quantity. The units of electric potential are volts. 1 volt = 1 J/C.

Just as we use the term "zero of potential" in talking about gravitational potential, we can also use that term to talk about voltage. We cannot solve a problem that involves voltage unless we know where the zero of potential is. Often, the zero of electric potential is called "ground."

Unless it is otherwise specified, the zero of electric potential is assumed to be far, far away. This means that if you have two charged particles and you move them farther and farther from each another, ultimately, once they're infinitely far away from each other, they won't be able to feel each other's presence.

The electrical potential energy of a charged particle is given by this equation:

Here, q is the charge on the particle, and V is the voltage.

It is extremely important to note that electric potential and electric field are not the same thing. This example should clear things up:

Electric field lines point in the direction that a positive charge will be forced, which means that our positron, when placed in this field, will be pushed from left to right. So, just as an object in Earth's gravitational field has greater potential energy when it is higher off the ground (think "mgh"), our positron will have the greatest electrical potential energy when it is farthest from where it wants to get to. The answer is A.

We hope you noticed that, even though the electric field was the same at all three points, the electric potential was different at each point.

This is a rather simple conservation of energy problem, but it's dressed up to look like a really complicated electricity problem.

As with all conservation of energy problems, we'll start by writing our statement of conservation of energy.

KEi + PEi = KEf + PEf

Next, we'll fill in each term with the appropriate equations. Here the potential energy is not due to gravity (mgh), nor due to a spring (1/2 kx2). The potential energy is electric, so should be written as qV.

Finally, we'll plug in the corresponding values. The mass of a positron is exactly the same as the mass of an electron, and the charge of a positron has the same magnitude as the charge of an electron, except a positron's charge is positive. Both the mass and the charge of an electron are given to you on the "constants sheet." Also, the problem told us that the positron's initial potential Vi was zero.

½ (9.1 × 10–31 kg)(6 × 106 m/s)2 + (1.6 × 10–19 C)(0) =
½ (9.1 × 10–31 kg)(1 × 106 m/s)2 + (1.6 × 10–19 C)(Vf)

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