Electric Potential (CIE A Level Physics)

• 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 lifted upwards and decreasing as 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 positive test charge moves closer to a negative charge, its electric potential decreases
  • When a positive test charge moves closer to a positive charge, its electric potential increases

  Work Done to Bring Like Charges Together

The electric potential V decreases in the direction of repulsion of the test charge and increases when moving towards each other

 Work Done to Separate Opposite Charges

The electric potential V decreases in the direction the test charge would naturally move in due to attraction and increases when the positive test charge moves away from the negative charge

• To find the potential at a point caused by multiple charges, add up each potential separately

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

• 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 to bring them together

• 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 to bring them together

• 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

The Potential Around a Charged Sphere

The potential changes as an inverse law with distance near a charged sphere