Force-Distance Graph (OCR A Level Physics): Revision Note

Force-Distance Graph for a Point Charge

• The key features of the force-distance graph are:

  • The values for F are all positive

  • As r increases, F against r follows a 1/r² relation (inverse square law)

  • The area under this graph is the work done ΔW

  • The graph has a steep decline as r increases

• The area under the graph can be estimated by counting squares, if it is plotted on squared paper, or by splitting it into trapeziums and summing the area of each trapezium

  • The inverse square law relation means that if the distance r increases by a factor of 2, F would decrease by a factor of 4

• This is a graphical representation of the equation:

$F=\frac{Qq}{4\mathrm{\pi }{\epsilon }_{\mathit{0}}{r}^{\mathit{2}}}$

• Where Q, q and 4πε₀ are constants