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Electricity and Magnetism
The Relation between Potential Difference and Electric Field Strength
For mathematical simplicity, we will consider a uniform field.
Consider moving a positive charge, Q, from point A to point B.
Let the magnitude of the potential difference between points A and B be v.
In moving a positive charge from A to B work is done by the field so the potential at B is less than the potential at A.
We will therefore represent the potential difference between A and B as -v.
Work done in moving the charge is w = F x
Work done per unit charge is potential difference, -v and
force per unit charge is electric field strength.
Therefore, the relation between potential difference and field strength is found by dividing the above equation by Q. After rearranging, we have