• 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