Question

$E={\displaystyle \frac{-dV}{dr}}$, here the negative sign signifies that

Answer 1

Explanation of the gradient of the potential,

1. The gradient of potential in an electric field and the distance between a point of charge are inversely proportional to each other.
2. The electric field occurs only if there is an electric potential difference.
3. A “test charge” is placed which causes a force between the two charges in the system.
4. We see the absence of an electric field if the charge is constantly distributed at all places, regardless of the electric potential.
5. The direction of the field is considered negative if it is directed from a greater potential to a lower potential.
6. Thus, “Electric field is the negative space derivative of electric potential” specifies the relationship between electric potential and electric field.

Thus, a negative sign in $E={\displaystyle \frac{-dV}{dr}}$ says that the direction of the electric field and the direction of potential is opposite.