The electric field = - potential gradient.
It comes from expressing energy changes in two different ways.
You can say work done = force x distance = qE x distance
However you can also say the work done = change in potential x charge moved = qV
If you equate these two different ways of expressing the same energy change you get
>qE x distance (d) = qV .. the q s cancel
>E x d = V
>E = V/d which is the potential gradient. The minus sign comes from the distance moved for a positive charge opposite the foield counts as being negative. ( You really need vectors to doi it properly).
>**To get a feel for this:**
>Lets consider gravity and a ball on a slope. The effective gravitational field could be indicated by the acceleration of the ball down the slope.
>The change in potential = mg(delta h) ie it depends on the change in height.
>so the ‘field = - potential gradient’ means the ball accelerates down the hill faster where the height changes a lot in a short distance.
>ie the ball accelerates down a steep hill. This is a very close analogy to electric fields and potentials.
 
 
Hope it helps
 
Regards
Arun
						

							
Dear student 
E x d = V
E = V/d which is the potential gradient. The minus sign comes from the distance moved for a positive charge opposite the foield counts as being negative. ( You really need vectors to doi it properly).
Good Luck