electric field e and electric potential v are relate as

Question

Arun · Answer

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

Vikas TU · Answer

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

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electric field e and electric potential v are relate as

electric field e and electric potential v are relate as

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