# relationship between electric potential and field strength?

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#1
In a past paper question I have been given a graph of electric potential against distance from point.

I have then been asked questions about the electric field strength and they are to be answered using the graph

I am not sure what the relationship between the two are?

Anyone want to to tell me and explain why? Thanks so much
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6 years ago
#2
(Original post by Mr Tall)
In a past paper question I have been given a graph of electric potential against distance from point.

I have then been asked questions about the electric field strength and they are to be answered using the graph

I am not sure what the relationship between the two are?

Anyone want to to tell me and explain why? Thanks so much
Mathematically, electric potential and field strength are connected by the fact that Electric potential, being a measure of work done per unit charge, is found from integrating the value for the electric field. This is because the field gives the force and work done is force x distance.
So if you integrate F (the field strength) wrt distance you get the potential. (Work done.)

So if this is the case, then the reverse is also true.
If you differentiate potential you get the field strength.
This is the origin of field strength is equal to potential gradient.

If you have a graph of potential against distance, the the gradient at any point will be equal to the force or field strength.
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