Electric Field

The electric field is a vector quantity that expresses the effect of source charges independent of any test charge. It is defined by rearranging Coulomb's force equation: the force on a test charge equals the test charge multiplied by the electric field. This approach allows us to describe charge interactions through an intermediate step, where a source charge creates a field that exerts force on other charges entering its vicinity.

The electric field direction is defined by the force a positive test charge would experience. A positive source charge repels the positive test charge, so its electric field points away from it. Conversely, a negative source charge attracts the positive test charge, so its electric field points toward it. This convention ensures consistent field direction regardless of which test charge is used.

When multiple source charges exist, the principle of superposition applies: the net electric field at any point is the vector sum of the individual electric fields from each source charge. Since Coulomb forces follow superposition, so does the electric field by definition. This allows calculation of complex field configurations by adding individual field contributions vectorially.

The SI unit of electric field is newton per coulomb (N/C). The electric field is a vector field because it has both magnitude and direction at every point in space. Each point has an associated electric field vector that describes the force per unit charge a test charge would experience at that location.

The electric field provides an intermediate framework for understanding Coulomb interactions. Instead of direct charge-to-charge forces, we imagine a source charge creating a field independent of other charges. When a second charge enters this field, it experiences a force based on the field strength at that point. This perspective separates the effect of the source charge from the response of the test charge.

The electric field is defined by treating the test charge as a point charge. In reality, charges are quantized with fundamental units being electron or proton charges, which are practically point charges with negligible spatial extent. This makes the point charge approximation excellent for most applications, since extended charges would experience different forces at different locations.

A negative test charge experiences a force opposite to the electric field direction. Since the field is defined by the force on a positive test charge, a negative charge moves opposite to the field vectors. This means negative charges are repelled by negative sources and attracted to positive sources, opposite to the field direction convention.