18.2.2 Electric 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 around a radial field or uniform field are perpendicular to the electric 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:

• 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 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
  • If the charge is negative, the potential increases with distance

• This is because the test charge is positive