Electric Field & Potential (Edexcel International A Level Physics)

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Electric Field & Potential

  • A positive test charge has electric potential energy due to its position in an electric field
  • The amount of electric potential energy depends on:
    • The magnitude of charge 
    • The value of the electric potential in the field


Work is done on a positive test charge Q to move it from the negatively charged plate A to the positively charged plate B. This means its electric potential energy increases

  • Electric potential is defined as the amount of work done per unit of charge at that point
  • A stronger electric field means the electric potential changes more rapidly with distance as the test charge moves through it
  • Hence, the relationship between the electric field strength and the electric potential is summarised as: 

The electric field strength is proportional to the gradient of the electric potential

  • This means: 
    • If the electric potential changes very rapidly with distance, the electric field strength is large
    • If the electric potential changes very gradually with distance, the electric field strength is small

  • An electric field can be defined in terms of the variation of electric potential at different points in the field:

The electric field at a particular point is equal to the gradient of a potential-distance graph at that point

  • The potential gradient in an electric field is defined as:

The rate of change of electric potential with respect to displacement in the direction of the field

  • The graph of potential V against distance r for a negative or positive charge is:

Electric Potential Gradient Graph, downloadable AS & A Level Physics revision notes

The electric potential around a positive charge decreases with distance and increases with distance around a negative charge

  • The key features of this graph are:
    • The values for V are all negative for a negative charge
    • The values for V are all positive for a positive charge
    • As r increases, V against r follows a 1/r relation for a positive charge and -1/r relation for a negative charge
    • The gradient of the graph at any particular point is the value of E at that point
    • The graph has a shallow increase (or decrease) as r increases

  • The electric potential changes according to the charge creating the potential as the distance r increases from the centre:
    • If the charge is positive, the potential decreases with distance
    • If the charge is negative, the potential increases with distance

Worked example

An electric field is set up between two pairs of oppositely charged plates, set X and set Y. 

A graph showing how the electric potential V varies with distance d is shown for both set X and set Y. 


State and explain which set creates the largest electric field strength.

Step 1: Recall the relationship between electric field strength and electric potential

    • The electric field strength is proportional to the gradient of the electric potential

Step 2: Interpret the gradient of the potential-distance graph

    • Set X has a larger gradient than set Y


Step 3: State and explain the conclusion

    • Set X creates a larger electric field strength
    • This is because the gradient of the potential between the plates is larger than it is for set Y

Exam Tip

Remember that whether the electric potential increases or decreases depends on the charge that is producing the potential! 

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