Obtain the relation between electric field and electric potential at a point
Obtain the relation between electric field and electric potential at a point
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).
For making it more understanding (do not write in exam)
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.
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).
For making it more understanding (do not write in exam)
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.
