Electric Potential Gradient (CIE A Level Physics)

• 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