The relation between electric field and electric potential can be understood through the concept of work done in moving a charge in an electric field.
- Electric Field:
- The electric field is a vector quantity that describes the force experienced by a positive test charge at a given point in space. It is defined as the force per unit positive charge at that point.
- Mathematically, electric field (E) is given by E = F/q, where F is the force experienced by the test charge q.
- Electric Potential:
- Electric potential is a scalar quantity that describes the work done in moving a positive test charge from infinity to a point in an electric field. It is defined as the electric potential energy per unit positive charge at that point.
- Mathematically, electric potential (V) is given by V = W/q, where W is the work done in moving the test charge q.
- Relation:
- The relationship between electric field and electric potential is given by the equation E = -dV/dr, where E is the electric field, V is the electric potential, and r is the distance from the point where the potential is being measured.
- This equation shows that the electric field is the negative gradient of the electric potential. In other words, the electric field points in the direction of the steepest decrease in the electric potential.
- Explanation:
- When a positive test charge is placed in an electric field, it experiences a force in the direction of the electric field lines. As the test charge moves in the direction of the electric field, it loses potential energy and gains kinetic energy.
- The electric potential at a point in the field represents the amount of work done in bringing a positive test charge from infinity to that point. The electric field, on the other hand, represents the force experienced by a positive test charge at that point.
- The negative sign in the relationship between electric field and electric potential indicates that the electric field points in the direction of decreasing potential. This relationship helps in understanding the behavior of charges in an electric field and how potential energy is converted into kinetic energy.