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The Relation between Potential Difference and Electric Field Strength
 For mathematical simplicity, we will consider a uniform field (as exists near the centre of the space between two parallel, oppositely charged metal plates). Consider moving a small positive charge, q, from point A to point B. Let the magnitude of the potential difference between points A and B be ΔV. 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 -ΔV. Work done, w moving the charge q is given by Now, work done per unit charge is the potential difference, -ΔV and force per unit charge is the electric field strength, E Therefore, the relation between potential difference and field strength is found by simply dividing the above equation by q. which is usually written as and the term in brackets is called the potential gradient, as it represents the slope (gradient) of a graph of potential against distance. This equation shows that alternative units for measuring field strength are Volts per metre, Vm-1 This means that the magnitude of the field strength between the two parallel plates is simply given by
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