In Electrostatics (Class 12 Physics), establishing the mathematical relationship between the Electric Field (E) and Electric Potential (V) is a highly important derivation and concept.
Because of this relationship, the unit of Electric Field can be written not only as Newtons per Coulomb (N/C) but also as Volts per metre (V/m).
The relation is expressed by the formula:
E = - dV / dr
Where:
The negative sign (-) in the formula E = -dV/dr is extremely important.
It indicates that the direction of the Electric Field is always in the direction of decreasing electric potential. In other words, an electric field always points from a higher potential region to a lower potential region.
Based on the formula, the electric field intensity at any point is equal to the negative of the potential gradient at that point.
An equipotential surface is a surface where the electric potential (V) is constant at all points. Therefore, the potential difference (dV) between any two points on it is zero.
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