Electric Potential

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Electric Potential

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

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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.
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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.

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  • 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
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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 .
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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.
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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.

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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.
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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.
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Positive or negative charge

  • The electrostatic potential-distance graphs mirror those of the gravitational potential-distance graphs.
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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}

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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