10.1.4 Equipotential Surfaces

• Equipotential lines (when working in 2D) and surfaces (when working in 3D) join together points that have the same gravitational potential
• These are always:
• Perpendicular to the gravitational field lines in both radial and uniform fields
• Represented by dotted lines (unlike field lines, which are solid lines with arrows)

• In a radial field (eg. a planet), the equipotential lines:
• Are concentric circles around the planet
• Become further apart further away from the planet

• In a uniform field (eg. near the Earth's surface), the equipotential lines are:
• Horizontal straight lines
• Parallel
• Equally spaced

• Potential gradient is defined by the equipotential lines

• No work is done when moving along an equipotential line or surface, only between equipotential lines or surfaces
  • This means that an object travelling along an equipotential doesn't lose or gain energy and ΔV =  0

Gravitational equipotential lines in a non-uniform and uniform gravitational field

Equipotential lines around a radial field or uniform field are perpendicular to the electric field lines

• The distinction between radial and uniform fields is an important one

• In a radial field (eg. a point charge), the equipotential lines:
• Are concentric circles around the charge
• Become further apart further away from the charge
• Remember: radial field is made up of lines which follow the radius of a circle

• In a uniform field (eg. between charged parallel plates), the equipotential lines are:
• Horizontal straight lines
• Parallel
• Equally spaced
• Remember: uniform field is made up of lines which are a uniform distance apart

Part (a)

• • • The lines of equipotential need to be perpendicular to the field lines at all times
    • These lines are almost circular when they are near the charges
    • And when moving out further the lines of equipotential cover both charges.

The lines of equipotential can be seen below

Part (b)

• • • It can be assumed that both charges are positive since the field lines point outwards.
    • It can also be assumed that the charge on the left has a larger charge than the charge on the right since:
      • It has a greater density of field lines
      • It has a larger sphere of influence shown by the lines of equipotential
      • The point of zero electric field strength between the two charges is closer to the right charge