Electric Equipotential Surfaces (HL) (HL IB Physics)

• Equipotential surfaces are lines of equal electric potential 
  • They are always perpendicular to the electric 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

• If a charge moves along an equipotential surface (or line), no work is done
  • This means the potential energy of the charge does not change

• Equipotential lines are used to represent potential gradient
• For example, for a positive point charge: 
  • The lines become closer together nearer the charge, this represents the potential gradient becoming steeper
  • If a positive test charge is pushed towards the charge, more work must be done to move it gradually closer

The left side image shows the equipotential lines for a point charge acting like contours on a map. They are perpendicular to the field lines, as shown on the right side image

• Equipotential surfaces can be drawn to represent the electric potential for a number of scenarios, such as
  • for a point charge
  • for multiple charges (up to four point charges)
  • inside and outside solid and hollow charged conducting spheres
  • between two oppositely charged parallel plates

Equipotential surface for a point charge

• In a radial field, such as around a point charge, the equipotential lines:
• are concentric circles around the charge
• become progressively further apart with distance

Equipotential lines for a radial electric field are concentric circles which increase in radius and are perpendicular to the field lines

• If a charged conducting sphere replaced a point charge, the equipotential surface would be the same 

Equipotential surface for multiple charges

• The equipotential surfaces for a dipole (two opposite charges) and for two like charges are shown below:

The equipotential surface for multiple charges can be obtained by drawing curves which are perpendicular to the field lines

• An equipotential surface between two opposite charges can be identified by a central line at a potential of 0 V
  • This is the point where the opposing potentials cancel

• An equipotential surface between two like charges can be identified by a region of empty space between them
  • This is the point where the resultant field is zero

Equipotential lines show that the potential has the greatest value near the charge and decreases with distance

Equipotential surface between parallel plates

• In a uniform field, such as between two parallel plates, the equipotential lines are:
• horizontal straight lines
• parallel
• equally spaced

The equipotential lines for a uniform field are evenly spaced parallel lines which are perpendicular to the field lines