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10.10 Electric Potential

The electric field can be described in terms of electric field intensity and electric potential. We have already described field in terms of electric intensity, in this section we will describe field in terms of electric potential or simply potential. In contrast to electric intensity, electric potential is a scalar quantity.

The potential at a point (in an electric field) is the external work needed to bring a positive unit charge, at constant speed, from the position of zero potential to the given point. Conventionally, the point of zero potential is taken at infinity.

The potential at a point is represented by symbol V. If VA and VB are the electric potentials of two points A and B, and if we are moving from point A to B, the potential difference is

DV = VB - VA

Once the potential difference between two points is known, the external work needed to move a charge q (with no change in its speed) from point A to B may be found

Wext = qDV = q(VB - VA)

The sign of this work depends on the sign of q and the relative magnitudes of VA and VB.

If Wext > 0, work is done by the external agent on the charge.

If Wext < 0, work is done on the external agent by the field. In this case, the external force acts opposite to the displacement of the charge.

The quantity DV depends only on the field set up by the source charges, not on the test charge.

The SI unit of potential is volt (V), which is equivalent to J/C.

The dimensions of V are

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The change in potential from point A to point B is

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If we choose V = 0 at r = ¥, the point A shift to the infinity. The potential at any point B in the field is given as

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Equipotential Surface

The locus of all the points, which have the same electric potential, is called an equipotential surface, or equipotential line.

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