Electric Potential Due to a Point Charge
- An electric field can be defined in terms of the variation of electric potential at different points in the field:
The electric field at a particular point is equal to the negative gradient of a potential-distance graph at that point
Equipotential Lines in Different Electric Fields
Equipotential lines around a radial field or uniform field are perpendicular to the electric field lines
- Equipotential lines are lines of equal electric potential
- The electric potential in an electric field is always drawn perpendicular to the field lines
- In a radial field, the equipotential lines are represented by concentric circles around the charge
- The equipotential lines become farther away from each other with increasing radius
- In a uniform electric field, the equipotential lines are equally spaced
Graph of Electric Potential, V Against Distance, r
The electric potential around a positive charge decreases with distance and increases with distance around a negative charge
- The electric potential changes according to the charge creating the potential as the distance r increases from the centre:
- If the charge is positive, the potential decreases with distance, r
- If the charge is negative, the potential increases with distance, r
- This is because the test charge is positive
Electric Potential Gradient
- The potential gradient in an electric field is defined as:
The rate of change of electric potential with respect to displacement in the direction of the field
- The potential gradient is defined by the equipotential lines
- The electric field strength is equivalent to a negative electric potential gradient and is given by the equation:
- Where:
- E = electric field strength (V m-1)
- ΔV = change in potential (V)
- Δr = displacement in the direction of the field (m)
- Hence, = electric potential gradient, i.e. the change in potential with distance
- The negative sign exists because the potential gradient acts in the opposite direction to the lines of force in the electric field
- The potential gradient is higher further away from the point charge
- The field strength is higher closer to the point charge
Exam Tip
One way to remember whether the electric potential increases or decreases with respect to the distance from the charge is by the direction of the electric field lines. The potential always decreases in the same direction as the field lines and vice versa.