4.16 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

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