• 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

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