Electricity and magnetism

Electric field and field lines

An electric field describes the electric force on a test charge; field lines show its direction, with their density indicating relative strength.

Charges establish electric fields in space. At a point, the force per unit positive test charge defines the electric-field vector $\vec E$. A field is a vector quantity: contributions from several source charges add vectorially.

Field lines and source charges

In a diagram, the conventional number of field lines leaving or entering a charge is proportional to its magnitude. Field lines are a visualization, not material threads. The superposition principle gives the total field by adding the field vectors from each source.

For a point charge $Q$, field magnitude falls as $1/r^2$, but its direction depends on the source sign: outward for $Q>0$ and toward the source for $Q<0$. For example, at a point $0.30$ m from a $+2.0\,\mu$C charge, $E=k|Q|/r^2\approx2.0\times10^5$ N/C. A $-1.0$ nC test charge there feels a force of magnitude $2.0\times10^{-4}$ N, opposite to the field vector. In symmetric arrangements, add vector components rather than adding magnitudes indiscriminately.

Finding the net electric field

Draw each source field vector at the observation point before calculating. Collinear vectors in the same direction add; opposite vectors subtract, leaving the direction of the larger one. For perpendicular vectors, use the Pythagorean theorem for the resultant magnitude. This procedure lets you find the force on any test charge from $\vec F=q\vec E_{\rm total}$ after determining the source field, independently of the test charge.

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