• 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