Electric fields

An electric field is a region around a charged object where a second object (neutral or charged) can “feel” an electric force between it and the first. The intensity of the field at any particular point depends on the charges and the distance between them.

To describe an electric field, we imagine that we are probing it with a unit test charge, a very small positive charge that you can think of as a proton on a stick. To represent all this in one drawing, we draw field lines around the charges to indicate the electric force of the unit test charge at all points. The field lines always leave (or enter) the circles perpendicular to the surface and go from positive to negative.

Electric field surrounding a positive charge and a negative charge (Wikimedia Commons)

Just as we use g\displaystyle \vec{g} in N/kg to describe the strength of a gravitational field, we use ϵ\displaystyle \vec{\epsilon} in N/C to describe the strength of an electric field:

ϵ=Felq2=kq1r2\displaystyle \vec{\epsilon} = \frac{\vec{F}_{\text{el}}}{q_{2}} = k \frac{q_{1}}{r^{2}}.

With g\displaystyle \vec{g}, the Earth is embedded in the number and the other mass is not (we multiply it to get the force). With ϵ\displaystyle \vec{\epsilon}, it’s the same deal, except we are talking about charges instead of masses.

When there are multiple charges with overlapping fields, we can calculate the net field strength by adding them all up:

ϵnet=ϵ1+ϵ2++ϵn\displaystyle \vec{\epsilon}_{\text{net}} = \vec{\epsilon}_{1} + \vec{\epsilon}_{2} + \cdots + \vec{\epsilon}_{n}.