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Potential in Electric Field

When the mass is moved above the ground level, work is done against the force of gravity and is equal to the product of force of gravity and vertical distance moved. This work done is added in the potential energy of the mass. Similarly if the mass is moved downward, work is done by the force of gravity and the potential energy of the mass is reduced by this amount of work done. Hence the potential energy or potential of the mass depends upon the position of the mass with respect t earth.

As already discussed, an electric charge causes an electric field around it which theoretically extends up to infinity. If any charge is introduced in this electric, field, it will be attracted or repelled according to the nature of the charge and when it will be moved, the work will be done against or by the force acting on the charge due to electric field. Hence potential in an electric field is exactly the same a sin the gravitational field.

In general political at any point in an electric is defined as the work done in moving a unit positive charge from infinity to that point.

Potential Deference

The potential difference between two points in an electric field is defined as the work done in moving a unit positive charge from the point of lower potential to the higher potential.

Unit potential Difference

If work done in bringing a positive charge of one coulomb from one point to another point in an electric field is one Joule then the potential difference between he two points is said to be unity (volt).

Potential Gradient

Practically the electric field intensity is not uniform, but varies from point to point. Let us consider that the electric field intensity between two points separated by a very small distance ds is constant and let it be E. The work done in moving unit + ve charge form one point to the other up the gradient of potential is Eds and therefore potential difference dv is given as

dv = - Eds

or E = dv = - g, potential gradient
Hence electric field intensity at any point is equal to the negative potential gradient as that point.

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