Question

For $E = \dfrac{{ - dV}}{{dr}}$, here the negative sign signifies ?

Answer 1

This question requires the conceptual understanding of the relationship between electric field and potential at a point in space. The electric field and potential difference are related to each other in a way that electric field increases in the direction in which potential decreases.

Complete answer:
The gradient of potential in an electric field is inversely proportional to the distance between a point of interest and a charge. Placing a second charge (a "test charge") in the system causes a force between the two charges (the field's units are Newtons, a measure of force per Coulomb), causing the charges to move relative to one another.

It's simpler to model interactions between two charges by considering one stationary and the other moving. If and only if there is an electric potential difference, the electric field occurs. There will be no electric field if the charge is uniform at all places, regardless of the electric potential.

Thus, “Electric field is the negative space derivative of electric potential” is a common expression for the relationship between electric field and electric potential.When a field is directed from a lower to a greater potential, the direction is assumed to be positive. The direction of the field is considered negative if it is directed from a greater potential to a lower potential.

Thus, a negative sign indicates that the direction of the electric field is in a direction opposite to potential.

Note: When numerous charges combine to form a field, the equipotential lines become distorted. Because the fields formed by each charge overlap, the potential is raised at any moment in comparison to the potential that would have resulted from either charge.