# What Is an Electric Field? Definition, Formula, Example

When a balloon is rubbed against a sweater, the balloon becomes charged. Because of this charge, the balloon can stick to walls, but when placed beside another balloon that has also been rubbed, the first balloon will fly in the opposite direction.

### Key Takeaways: Electric Field

• An electric charge is a property of matter that causes two objects to attract or repel depending on their charges (positive or negative).
• An electric field is a region of space around an electrically charged particle or object in which an electric charge would feel force.
• An electric field is a vector quantity and can be visualized as arrows going toward or away from charges. The lines are defined as pointing radially outward, away from a positive charge, or radially inward, toward a negative charge.

This phenomenon is the result of a property of matter called electric charge. Electric charges produce electric fields: regions of space around electrically charged particles or objects in which other electrically charged particles or objects would feel force.

## Electric Charge Definition

An electric charge, which can be either positive or negative, is a property of matter that causes two objects to attract or repel. If the objects are oppositely charged (positive-negative), they will attract; if they are similarly charged (positive-positive or negative-negative), they will repel.

The unit of electric charge is the coulomb, which is defined as the amount of electricity that is conveyed by an electrical current of 1 ampere in 1 second.

Atoms, which are the basic units of matter, are made of three types of particles: electrons, neutrons, and protons. Electrons and protons themselves are electrically charged and have a negative and positive charge, respectively. A neutron is not electrically charged.

Many objects are electrically neutral and have a total net charge of zero. If there is an excess of either electrons or protons, thus yielding a net charge that is not zero, the objects are considered charged.

One way to quantify electrical charge is by using the constant e = 1.602 *10-19 coulombs. An electron, which is the smallest quantity of negative electrical charge, has a charge of -1.602 *10-19 coulombs. A proton, which is the smallest quantity of positive electrical charge, has a charge of +1.602 *10-19 coulombs. Thus, 10 electrons would have a charge of -10 e, and 10 protons would have a charge of +10 e.

## Coulomb's Law

Electric charges attract or repel each other because they exert forces on each other. The force between two electric point charges—idealized charges that are concentrated at one point in space—is described by Coulomb’s law. Coulomb's law states that the strength, or magnitude, of the force between two point charges is proportional to the magnitudes of the charges and inversely proportional to the distance between the two charges.

Mathematically, this is given as:

F = (k|q1q2|)/r2

where q1 is the charge of the first point charge, q2 is the charge of the second point charge, k = 8.988 * 109 Nm2/C2 is Coulomb’s constant, and r is the distance between two point charges.

Although there are technically no real point charges, electrons, protons, and other particles are so small that they can be approximated by a point charge.

## Electric Field Formula

An electric charge produces an electric field, which is a region of space around an electrically charged particle or object in which an electric charge would feel force. The electric field exists at all points in space and can be observed by bringing another charge into the electric field. However, the electric field can be approximated as zero for practical purposes if the charges are far enough from each other.

Electric fields are a vector quantity and can be visualized as arrows going toward or away from charges. The lines are defined as pointing radially outward, away from a positive charge, or radially inward, toward a negative charge.

The magnitude of the electric field is given by the formula E = F/q, where E is the strength of the electric field, F is the electric force, and q is the test charge that is being used to “feel” the electric field.

### Example: Electric Field of 2 Point Charges

For two point charges, F is given by Coulomb’s law above.

• Thus, F = (k|q1q2|)/r2, where q2 is defined as the test charge that is being used to “feel” the electric field.
• We then use the electric field formula to obtain E = F/q2, since q2 has been defined as the test charge.
• After substituting for F, E = (k|q1|)/r2.

## Sources

• Fitzpatrick, Richard. “Electric Fields.” The University of Texas at Austin, 2007.
• Lewandowski, Heather, and Chuck Rogers. “Electric Fields.” University of Colorado at Boulder, 2008.
• Richmond, Michael. “Electric Charge and Coulomb’s Law.” Rochester Institute of Technology.
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