Question

The relation between the electric field \[\vec{E}\] and the potential gradient is expressed as:

Options

• \[\vec{E} = -\frac{dV}{dr}\]

• \[\vec{E} = +\frac{dV}{dr}\]

• \[\vec{E} = -\frac{d^2V}{dr^2}\]

• \[\vec{E} = V \cdot r\]

Answer 1

The electric field is the negative of the potential gradient: \[\vec{E} = -\frac{dV}{dr}\]. The negative sign indicates that the field points from high potential to low potential. A greater E means the potential changes faster (denser equipotential surfaces), while a weaker E means the potential changes slowly (surfaces farther apart).