We have discussed the electric field and potential. Electric potential is a scalar quantity but electric field is a vector quantity. How are these quantities related to each otehr?
To derive the relation between electric field and potential let us consider two closely spaced equipotential surfaces A and B as shown in figure with potential values V and V +dow V , where Dow V is the change in V in the direction of electric field E. Let P be a point on the surface B. dow l is the perpendicular distance of the surface A from P. Imagine that a unit positive charge is moved along this perpendicular from the surface B to surface A against the electric field. The work done in this process is |E | dow l
We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest. (ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point
To derive the relation between electric field and potential let us consider two closely spaced equipotential surfaces A and B as shown in figure with potential values V and V +dow V , where Dow V is the change in V in the direction of electric field E. Let P be a point on the surface B. dow l is the perpendicular distance of the surface A from P. Imagine that a unit positive charge is moved along this perpendicular from the surface B to surface A against the electric field. The work done in this process is |E | dow l
We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest. (ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point
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