# 4.16 Electric Field & Potential

## 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

#### 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! ### Get unlimited access

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