Electric Field & Potential (Edexcel A Level Physics) : Revision Note

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:

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