CIE A Level Physics (9702) 2019-2021

Revision Notes

21.2.2 Electric Potential Gradient

Potential Gradient

  • 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

  • The potential gradient is defined by the equipotential lines
    • These demonstrate the electric potential in an electric field and are always drawn perpendicular to the field lines
  • Equipotential lines are lines of equal electric potential
    • Around a radial field, the equipotential lines are represented by concentric circles around the charge with increasing radius
    • The equipotential lines become further away from each other
    • In a uniform electric field, the equipotential lines are equally spaced
  • 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 electric field strength is equivalent to this, except with a negative sign:

Potential Gradient equation

  • Where:
    • E = electric field strength (V m-1)
    • ΔV = change in potential (V)
    • Δr = displacement in the direction of the field (m)
  • The minus sign is important to obtain an attractive field around a negative charge and repulsive field around a positive 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
    • If the charge is negative, the potential increases with distance
  • This is because the test charge is positive

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.

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