CIE A Level Physics (9702) 2019-2021

Revision Notes

21.2.1 Electric Potential

Electric Potential

  • In order to move a positive charge closer to another positive charge, work must be done to overcome the force of repulsion between them
  • Energy is therefore transferred to the charge that is being pushed upon
    • This means its potential energy increases
  • If the positive charge is free to move, it will start to move away from the repelling charge
    • As a result, its potential energy decreases back to 0
  • This is analogous to the gravitational potential energy of a mass increasing as it is being lift upwards and decreasing and it falls
  • The electric potential at a point is defined as:

The work done per unit positive charge in bringing a small test charge from infinity to a defined point

  • Electric potential is a scalar quantity
    • This means it doesn’t have a direction
  • However, you will still see the electric potential with a positive or negative sign. This is because the electric potential is:
    • Positive when near an isolated positive charge
    • Negative when near an isolated negative charges
    • Zero at infinity
  • Positive work is done by the mass from infinity to a point around a positive charge and negative work is done around a negative charge. This means:
    • When a test charge moves closer to a negative charge, its electric potential decreases
    • When a test charge moves closer to a positive charge, its electric potential increases
  • To find the potential at a point caused by multiple charges, add up each potential separately

Electric Potential Due to a Point Charge

  • The electric potential in the field due to a point charge is defined as:

Electric Potential Due to a Point Charge equation

  • Where:
    • V = the electric potential (V)
    • Q = the point charge producing the potential (C)
    • ε0 = permittivity of free space (F m-1)
    • r = distance from the centre of the point charge (m)
  • This equation shows that for a positive (+) charge:
    • As the distance from the charge r decreases, the potential V increases
    • This is because more work has to be done on a positive test charge to overcome the repulsive force
  • For a negative (−) charge:
    • As the distance from the charge r decreases, the potential V decreases
    • This is because less work has to be done on a positive test charge since the attractive force will make it easier
  • Unlike the gravitational potential equation, the minus sign in the electric potential equation will be included in the charge
  • The electric potential changes according to an inverse square law with distance
  • Note: this equation still applies to a conducting sphere. The charge on the sphere is treated as if it concentrated at a point in the sphere from the point charge approximation

Worked example: Van de Graaf charge

Electric_Potential_Due_to_a_Point_Charge_Worked_Example_-_Van_de_Graaf_Charge_Question, downloadable AS & A Level Physics revision notes

Part (a)

Step 1:            Write down the known quantities

Radius of the dome, r = 15 cm = 15 × 10-2 m

Potential difference, V = 240 kV = 240 × 103 V

Step 2:            Write down the equation for the electric potential due to a point charge

Electric Potential Due to a Point Charge equation

Step 3:            Rearrange for charge Q

Q = V4πε0r

Step 4:            Substitute in values

Q = (240 × 103) × (4π × 8.85 × 10-12) × (15 × 10-2) = 4.0 × 10-6 C = 4.0 μC

Part (b)

 Step 1:            Write down the known quantities

Q = charge stored in the dome = 4.0 μC = 4.0 × 10-6 C

r = radius of the dome + distance from the dome = 15 + 30 = 45 cm = 45 × 10-2 m

Step 2:            Write down the equation for electric potential due to a point charge

Electric Potential Due to a Point Charge equation

Step 3:            Substitute in values

Electric Potential Due to a Point Charge Worked Example equation

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