Graphical Representation of Electric Potential

• What can an electric field be described in terms of?

  The variation of electric potential
• What is the potential gradient of an electric field?

  The rate of change of electric potential
• How is the potential gradient defined?

  Change of potential with respect to displacement
• What does a graph of potential V against distance r represent?

  It represents the electric potential of a charge

  
• What is the equation for electric potential V?

  V = $\frac{Q}{4\pi\epsilon_0 r}$
• What does the gradient of the V-r graph represent?

  The electric field strength E at that point

  
• How can the electric field strength E be mathematically expressed?

  E = $-\frac{\Delta V}{\Delta r}$
• What does the negative sign in the equation for E indicate?

  Field strength opposes increasing potential
• How does electric potential behave around a positive charge?

  It decreases with distance
• How does electric potential behave around a negative charge?

  It increases with distance
• What are the key features of the V-r graph for charges?

  • Negative potential for negative charge
  • Positive potential for positive charge
  • Follows a 1/r relation for positive charge
  • Follows a -1/r relation for negative charge
  • Gradient equals field strength E
  • Curve is shallower than E-r graph

  
• How can potential difference be determined from a field-distance graph?

  By calculating the area under the graph
• What is the equation for electric field strength E?

  E = $\frac{Q}{4\pi\epsilon_0 r^2}$
• What relationship does electric field strength E have with distance r?

  E has a 1/r relationship

  
• What are the key features of the E-r graph for charges?

  • Negative field strength for negative charge
  • Positive field strength for positive charge
  • Follows a 1/r relation (inverse square law)
  • Area under graph equals potential difference ΔV
  • Curve is steeper than V-r graph

  
• What is a good way to revise equations and graphs in this topic?

  • Organize knowledge in a resonant way
  • Use diagrams and charts
  • Practice with past exam questions