What Electrical potential energy?

Answer 1

Electric potential is like electric potential energy, except electric potential energy requires that you have at least two charged particles: one charged particle (can be considered to be stationary) to produce the electric field and another charged particle to be affected by that electric field.

If both charged particles are positively charged, then when you move the nonstationary charged particle closer to the stationary charged particle, potential energy of the system increases, because the charged particles naturally want to repel.

However, let's say you remove that nonstationary charged particle and are left with just the single charged particle. There is no more potential energy in the system, because there is no other charged particle to be acted upon by the electric field. However, the single charged particle still emits an electric field. This field is what creates "electric potential." Even though there is no second particle in the system, if you were to place a second particle into the system (let's call it a test particle), its potential energy would be equal to the electric potential multiplied by the charge of the test particle.

U = kq1q2/r (electric potential energy with 2 charges, where the 0 of potential energy is infinitely far away)

V = kq1/r (electric potential requiring only 1 charge)

V = U/q2 (electric potential is potential energy without the second charge)

U = Vq2 (electric potential energy is electric potential multiplied by second charge)

There is also a concept called gravitational potential, where it's gravitational potential energy divided by the test mass.

It can be a negatively charged particle. In that case, electric potential decreases as you get closer to the negatively charged particle. Even though electric potential decreases, if you have two negatively charged particles, electric potential energy increases as you move the 2nd negative charge closer to the first charge. This is because multiplying 2 negative charges makes a positive:

U = k(-q1)*(-q2)/r = kq1q2/r (assuming q1 and q2 are the charge magnitudes)

So in this case, it's a little weird because that's how the math works. Nature has a tendency to reduce potential energy, but potential is different and doesn't work the same way.

However if the test charge was positive, the sign of electric potential energy will be the same as electric potential with respect to location.

V = k(-q1)/r = -kq1/r

U = k(-q1)(q2)/r = -kq1q2/r

Potential energy is not the same as potential! They are related, but don't get them confused. Energy is measured in Joules. Potential is measured in Volts. Completely different units.

Volts = Number of Joules / Number of Coulombs.

Electric Potential = Electric Potential Energy / Charge of Test Particle