Question

Relations between field & potential

It's mathematical proof

Answer 1

Hence electric field is the negative gradient ofthe scalar potential. The negative sign came as a result because the potential difference is the work done per unit charge against the electrostatic force to move a charge from a to b. However, this equation is valid only for static electrostatic fields.

Answer 2

Heya.........

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QUESTION:- relation btw field and potential

Mathematical proof?

ANSWER
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A , B= closely spaced equipotential surface

V ,V +delta V = potential of A and B respectively

Delta V = change in V in the direction of the electric field

P= a point on the surface B
DeltaL = perpendicular distance of the surface A and P

Work done in moving a unit positive charge from B to A is E delta I

This work done equals the. Potential difference Va -Vb

E delta I = V-(V+ delta V) = -delta V

E=-delta V/ delta L

This can show that electric charge is negative gradient of potential
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Hope it helps
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