Properties of Line of Electric Force

Theorem

Lines of electric force have the following properties:

Line of Electric Force is Continuous

Let $\mathbf E$ be an electric field.

Let $L$ be a line of force within $\mathbf E$.

Then, except for the positive charge or negative charge at which $L$ may start or end, $L$ is continuous.

Lines of Electric Force do not Cross

Let $\mathbf E$ be an electric field.

Let $L_1$ and $L_2$ be lines of force within $\mathbf E$.

Then $L_1$ and $L_2$ do not cross over each other.

Direction of Line of Electric Force

Let $\mathbf E$ be an electric field.

Let $L$ be a line of force within $\mathbf E$.

Then $L$ has one of the following properties:

$(1): \quad$ Begins on a positively charged body and ends on a negatively charged body

$(2): \quad$ Begins on a positively charged body and goes to infinity without terminating

$(3): \quad$ Comes from infinity without a start point and ends on a negatively charged body.

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.2$ The Electric Field