Question

show that the electric field intensity at a point can be given as negative of potential gradient​

Answer 1

The electric field intensity at a point is equal to the negative of potential gradient​:

Explanation:

• The approach is to imagine moving a charge from purpose A to purpose B

• Where there's a possible distinction between the 2 points. (Easiest to imagine in Associate in Nursing static field- however it needn't be the case)

• If you progress a charge letter of the alphabet through this potential, then

work done =Q x Δ V

where

Δ V= modification in potential difference

Force on charge is given by

F = QE  

where

E = electric field strength

q = charge

Now, Work done = force x distance

∴ W = Fs

Work done = -QEd

               W =  -Q E Δx

where

Δx is modification in position

Now we are able to equate the 2 ways for shrewd work done

-QE= letter of the alphabet Δ        

V (Q will cancel)

-E  Δx =  ΔV

This shows that the electric field intensity at a point can be given as negative of potential gradient​.