Electric Potential for a Radial Field (Edexcel International A Level (IAL) Physics): Revision Note

Electric Potential for a Radial Field

Electric Potential Energy

• In order to move a positive charge closer to another positive charge, work must be done to overcome the force of repulsion between them

  • Similarly, to move a positive charge away from a negative charge, work must be done to overcome the force of attraction 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 charge in bringing a positive test charge from infinity to that 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 around an isolated positive charge

  • negative around an isolated negative charge

  • zero at infinity

• Positive work is done to move a positive test charge from infinity to a point around a positive charge and negative work is done to move it to a point 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

The electric potential V is positive at all points around a positive charge and negative at all points around a negative charge, and its magnitude increases closer to the charge

Electric Potential due to a Point Charge

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

$V=\frac{Q}{4\mathrm{\pi }{\epsilon }_{0}r}$

• 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)

• The sign of V depends on the charge Q producing the potential, not on any test charge placed in the field:

  • For a positive charge Q, the potential is positive and increases (becomes more positive) as the distance r decreases

  • For a negative charge Q, the potential is negative and decreases (becomes more negative) as the distance r decreases

• Unlike the gravitational potential equation, the electric potential can be positive or negative, because Q can be positive or negative

• The electric potential varies according to 1 / r

  • Note, this is different to electric field strength, which varies according to 1 / r²