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Electric Potential

Physics: AQA A Level, topic 7.3.4

Electric Potential

Electric potential is the work done to move a positive test charge from infinity to a given point within the field.

Work done

Work done

  • Electric potential is the work which you need to do to bring a positive point charge to a distance, r, from the charge making the field.
  • The potential at infinity is zero.
  • The potential is largest right next to the charge.
Calculating the potential

Calculating the potential

  • Electric potential = constant x charge ÷ distance
  • V=14πϵ0×QrV=\frac{1}{4{\pi}{{\epsilon}_0}}{\times}\frac{Q}{r}
  • Potential is proportional to 1r\frac{1}{r} so falls off more slowly than force or field

Moving in an Electric Field

In order to move a charge through a field, work must be done as the energy of the charge will change.

Equipotentials

Equipotentials

  • An equipotential line or surface is one on which the voltage is constant.
  • This means that there is no change in potential difference or energy if a charge just moves along this line or surface.
  • No work is done if a charge moves along an equipotential.
  • Equipotential lines are placed at equal intervals of energy
Point charge equipotential

Point charge equipotential

  • For a charge equipotential lines are circles of constant radius.
  • As the lines get further from the charge the gaps between the lines get larger .
Parallel plate equipotential

Parallel plate equipotential

  • For parallel plates, equipotential lines are straight lines parallel to the plates.
  • These straight lines are evenly spaced as the field is uniform.
Work done

Work done

  • Work done to move a charge = charge x change in potential difference
  • W=QΔVW=Q{\Delta}V
  • If the charge is moved between equipotential lines then work is done.
  • ΔV{\Delta}V can be found by finding the area under a field-distance graph.

Electric Potential Graph

Gravitational potentials and electrostatic potentials have very similar graphs.

Comparison to gravitational potential

Comparison to gravitational potential

  • The gravitational field strength around a point mass and the electrostatic field around a point charge have the same patterns, although they are different magnitudes.
  • The formulae for the relationship between the field strength and distance both include inverse-squares.
  • The significant difference is that electrostatic fields can have either positive or negative values, indicating that the force can either be repulsive or attractive respectively.
Calculating work done

Calculating work done

  • Just like in the gravitational case, the work done in moving a positive charge away from a central positive charge can be calculated by finding the area underneath the appropriate curve.
Positive or negative charge

Positive or negative charge

  • The electrostatic potential-distance graphs mirror those of the gravitational potential-distance graphs.
Positive or negative charge 2

Positive or negative charge 2

  • In both cases, the magnitude of the electrostatic potential is given by:
  • V=Q4πϵ0rV=\frac{Q}{4\pi \epsilon_0 r}

Test yourself on Electric Potential

  • What is the correct equation for the electric potential?

  • What is the electric potential at infinity?

  • How much work is done if a charge is moved along an equipotential?

  • What is the correct equation for work done?

  • What is the relationship between field strength and distance in electric potential graphs?

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