Electric Potential Energy and Potential Difference

Electric potential energy results from forces between charges; potential difference is the energy needed to move a charge from point A to B.

Learning Objective

Calculate the potential energy between the charges

Key Points

Electric potential energy is a type of potential energy that results from Coulomb forces. The potential energy (UE) between charges q and Q can be calculated as a function of distance between the charges (r): $U_E(r)=\frac {qQ}{4 \pi \epsilon_0 r}$.
The formula for potential energy can be modified for potential between many charges, so long as the interactions of each charge with every other charge in the system are considered. For example, potential between three charges can be solved using the following formula: $U_E=\frac {1}{4 \pi \epsilon_0 r} (\frac {Q_1Q_2}{r{12}}+\frac {Q_2Q_3}{r{23}}+\frac {Q_1Q_3}{r{13}})$.
Potential difference, or voltage, is the difference in electric potential energy between two points. It is denoted by ∆V and has units of volts, or joules per Coulomb.

Terms

coulomb
In the International System of Units, the derived unit of electric charge; the amount of electric charge carried by a current of 1 ampere flowing for 1 second. Symbol: C
potential energy
The energy an object has because of its position (in a gravitational or electric field) or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)

Full Text

Electric potential energy is a type of potential energy that results from Coulomb forces. It is measured in joules and depends on the positioning of charged particles relative to one another, as well as the magnitude of their respective charges.

The potential energy (U_E) between charges q and Q can be calculated as a function of distance between the charges (r):

$U_E(r)=\frac {qQ}{4 \pi \epsilon_0 r}$

If there are three or more charges, the above formula can be modified so that the potential energies between all charges are summed. Consider, for example, the case involving charges Q₁, Q₂ and Q₃:

$U_E=\frac {1}{4 \pi \epsilon_0 r} (\frac {Q_1Q_2}{r{12}}+\frac {Q_2Q_3}{r{23}}+\frac {Q_1Q_3}{r{13}})$

In this example, r₁₂ represents the distance between Q₁ and Q₂, r₂₃ represents the distance between Q₂ and Q₃, and r₁₃ represents the distance between Q₁ and Q₃. The above formula can be modified for any number of charges.

Potential Difference

Potential difference , or voltage, is the difference in electric potential energy between two points. It is denoted by ∆V and has units of volts, or joules per Coulomb.

Electric Potential Difference

A brief overview of electric potential difference and electric potential energy for beginning physics students.

Voltage denotes the work per unit charge that must be done against a static electric field to move a charge from one point to another. It may represent a source of energy, or lost, stored or used energy. Voltage also is defined such that negative charges are pulled towards higher voltages, while positive charges move towards lower voltages. Thus, current in wires flows from higher to lower voltages.

Potential difference is independent of path taken from one point to another, and may be measured by any of a number of instruments . These include the voltmeter, the potentiometer, and the oscilloscope. It is most typically measured in circuits, and in such situations can be calculated using Ohm's Law, which will be covered in a later atom.

Potential difference in a static field

When a charge q moves from point A to point B, the potential difference is independent of path taken.

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