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electric field e and electric potential v are relate as electric field e and electric potential v are relate as
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 distanceHowever you can also say the work done = change in potential x charge moved = qVIf 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 RegardsArun
Dear student E x d = VE = 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
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