Lines of Electric Force do not Cross
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Theorem
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.
Proof
Follows directly from Vector Lines do not Intersect.
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