## Chapter 17: Electric Potential

Note: To understand this chapter, you must first have understood the concept of electric field, which is covered in the previous chapter.

## Electric Potential Energy

**Electric potential energy**is the potential energy for the electrostatic force.

**Electric potential is the electric potential energy per unit charge.**

V = PE/q

But only differences in potential energy are

**meaningful**; only the

**difference in potential (potential difference)**is measurable.

V = △PE/q = W / q = qEd / q = Ed

From this equation, we can see that the unit of potential difference is the unit of energy, joules (J), divided by the unit of charge, coulomb (C), or J/C, and we give it a new name,

**volt (V)**. We also give potential difference a simplified name,

**voltage**.

## Equipotential Lines

Unlike like electric field lines, which originate from the charge and goes outward if the charge is positive and goes inward if the charge is negative, equipotential lines are concentric circles (circles with one center).

Here, electric field line is shown in golden, equipotential lines are shown in blue. Electric field and force are both vectors, but electric potential is a scalar.

Here, electric field line is shown in golden, equipotential lines are shown in blue. Electric field and force are both vectors, but electric potential is a scalar.

## Electron volt

The name “electron volt” (eV) might suggest that it is a measurement of voltage, but it is actually a unit of energy. 1 eV = 1.6*10^-19 J

It is defined as the energy acquired by a particle carrying a charge whose magnitude equals that on the electron as a result of moving through a potential difference of 1V.

It is defined as the energy acquired by a particle carrying a charge whose magnitude equals that on the electron as a result of moving through a potential difference of 1V.

## Electric potential due to point charges

The electric potential at a distance r from a single point charge Q is determined by this equation:

V = kQ / r , (k = 9*10^9 N*m^2/C^2)

Assuming that Q is constant, as the distance r increases, the electric potential V decreases. V varies inversely as r. Recall that electric field varies inversely as r^2.

What about the electric potential in a charged sphere? Recall in chapter 16 that electric field is zero within the sphere, but the electric potential is a constant (kQ/r) within the sphere.

V = kQ / r , (k = 9*10^9 N*m^2/C^2)

Assuming that Q is constant, as the distance r increases, the electric potential V decreases. V varies inversely as r. Recall that electric field varies inversely as r^2.

What about the electric potential in a charged sphere? Recall in chapter 16 that electric field is zero within the sphere, but the electric potential is a constant (kQ/r) within the sphere.

## Capacitor and capacitance

A capacitor is a device that can store electric charge, and consists of two conducting objects placed near each other but not touching. If a voltage is applied across a capacitor, the two plates are charged. Charge is accumulated on each plate, and it is found that the amount of charge Q is directly proportional to the magnitude of the potential difference V between them.

Q = kV, and we name this constant k, capacitance.

Q = kV, and we name this constant k, capacitance.

**Thus, Q = CV C = Q/V****Capacitance**is measured in coulombs per volt, and is given a new name called**farad**(F).**What determines the capacitance of a capacitor?**

The larger each plate is, the more charge it can store on the plate, and it is found that capacitance is directly proportional to the area of the plate. The capacitance is also inversely directly proportional to the distance between two plates. Thus, the capacitance is determined by this equation. The constant has the value 8.85 * 10^ -12 C^2 /N*m^2

## Storage of electric energy

As the capacitor accumulates the charge, its electric energy is also increasing. The QV graph is a upward sloping curve with a constant slope, capacitance. The area under the QV graph then, is the electric energy.

PE = 1/2 QV = 1/2 CV^2 = Q^2 / (2C)

PE = 1/2 QV = 1/2 CV^2 = Q^2 / (2C)