What does "Electric potential is the negative line integral of electric field" mean?

Expert Solution

The multiplication of electric field and the path length gives Line integral of electric Field.

Let there be two point A and B on a non uniform electric field (magnitude and direction at every point is different). The irregular line denotes the path travelled by charge. With changing Electric field, the path travelled by a charge also changes at every point on the curve.

To find line integral at every point, take a very small length dl on the path. So that dl makes a certain angle θ with the electric field. On resolving dl into two components as dlcosθ and dlsinθ the component

of dl along E is dl cosθ. As shown in figure.

Potential difference dV = Edr.

So line integral to move charge from A to B = A∫BEdrCosθ

VA - VB = A∫B E→.dr→

To move charge from B to A (VA - VB) = - B∫AE→.dr→

In a variable electric field, potential difference between two point is equal to negative of line integral of electric field.

genius_generous answered 5 months ago

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