Electric Field
Electricity and Magnetism

## Electric field

Glossary Definition for 16-19 #### Description

An electric field exists in any region where a charged particle is subject to a force that depends only on the particle’s charge and position.

The electric field at a point is a vector quantity usually represented by the symbol E.

The electric field at a point is defined as the force per unit charge that would act on a small positively charged particle located at that point.

If a small test charge of size q is subject to a force F at some point, and F depends only on the particle’s charge and position, then the electric field at that point is defined as

E = Fq

#### Discussion

Electric field is sometimes referred to as electric field strength; this glossary avoids that term because it might be confused with the magnitude of the electric field.

Representing electric fields

Electric fields can be represented graphically by electric field lines and/or by equipotentials.

Electric field lines represent the direction and magnitude of an electric field throughout some region of three-dimensional space. The field lines are continuous unless the region contains charges on which the field lines can begin or end. The orientation of the field lines indicates the direction of the electric field. A strong field is represented by field lines drawn close together; the more closely spaced, the stronger the field.

Equipotentials join points that are all at the same potential. In three-dimensional space, the equipotentials are surfaces, but they are often represented by lines in a two-dimensional ‘slice’ through the region. Equipotentials are usually drawn so that there is a constant electrostatic potential difference between each one and its neighbours. The spacing between equipotentials indicates the magnitude of the field; the closer the equipotentials, the greater the potential gradient – in other words, the stronger the field.

The field line at any point is always normal to the equipotential drawn through that point. The field direction is from high to low electrostatic potential

Figure 1 shows field lines and equipotentials for a uniform electric field between two parallel plates. Figure 1: Field lines (solid arrows) and equipotentials (dotted lines) for an electric field between two parallel oppositely charged conducting plates

Figure 2 shows the radical field of an isolated point charge, or a spherical distribution of charge. If the charge is positive the field is directed radially outwards; if it is negative the field is directed radially inwards. Figure 2: The electric field due to a positive charged spherical object

#### SI units

newton per coulomb, N C-1; volt per metre, V m-1

kg m s-3 A-1

#### Mathematical expressions

• If a test charge q is subject to an electrostatic force F at some point, then the electric field at that point is defined by

E  =  F q
• At any point located a distance r from a point charge Q in free space (a vacuum) the magnitude of the electric field due to the point charge is

E = Q4 π ε 0r 2

where ε 0 is the permittivity of free space and the field acts in a radial direction as shown in figure 2.
• If there is an electrostatic potential difference ΔV between two infinite parallel conducting plates separated by a distance d then there is a uniform electric field between the plates and its magnitude is

E = ΔVd
• More generally, the x component of an electric field is

Ex = − dVdx

and similarly for the y and x components

#### Related entries

• Charge
• Electrostatic potential
• Force
• Potential difference, electrostatic

#### In Context

In liquid crystal displays (LCDs) electric fields are used to control the orientation of long molecules that have a small positive charge at one end and a small negative charge at the other. The magnitude of the field used in LCDs is typically ~ 106 N C-1. An electron has charge q = -1.60 × 10-19 C, so when located in a field of this magnitude an electron experiences a force that acts in the opposite direction to that of the field and has magnitude F = 1.60 × 10-13 N. Close to the Earth’s surface, there is a naturally occurring electric field of about 150 N C-1, which becomes weaker with increasing altitude. The field direction is vertically downwards – the Earth is negatively charged whereas the atmosphere has a net positive charge. The field is produced and maintained by various processes including the interactions of cosmic rays and the solar wind (a stream of charged particles) with the atmosphere, and radioactivity within the Earth.

###### Electric Field
can be analysed using the quantity Electrostatic Potential
can be represented by Field Line