Electric Potential Energy of Two Point Charges
Work Done
- Work is done when:
- A positive charge moves in the same direction as the electric field lines in an electric field
- A negative charge moves in the opposite direction to the electric field lines in an electric field
- The work done in moving a charge Q is equal to the electric potential energy
- The work done is calculated by the equation:
- Where:
- W = work done (J)
- V = electric potential due to a point charge (V)
- Q = charge (C)
Electric Potential Energy
- The electric potential energy Ep at a point in an electric field is defined as:
The work done in bringing a charge from infinity to that point
- The electric potential energy of a pair of point charges Q1 (charge that is producing the electric field) and Q2 (charge that is moving in the electric field) is defined by:
- Where:
- Ep = electric potential energy (J)
- Q1 = charge that is producing the electric field (C)
- Q2 = charge that is moving in the electric field (C)
- r = separation of the charges Q1 and Q2 (m)
- ε0 = permittivity of free space (F m-1)
- Unlike the electric potential, the electric potential energy will always be positive
- Recall that at infinity, V = 0 therefore Ep = 0
Electric Potential Energy for a Moving Positive and Negative Charge
Work is done when moving a point charge away from another charge. E.P.E is another way of saying electric potential energy
Change in Electric Potential Energy
- It is more useful to find the change in electric potential energy when one charge moves away from another
- The change in electric potential energy from a charge Q1 at a distance r1 from the centre of charge Q2 to a distance r2 is given by the equation:
- The change in electric potential, ΔV, from charge Q1 is:
- Both equations are similar to the change in gravitational potential between two points near a point mass
Worked example
An α-particle is moving directly towards a stationary gold nucleus .
At a distance of 4.7 × 10−15 m the α-particle momentarily comes to rest.
Calculate the electric potential energy of the particles at this instant.
Answer:
Step 1: Write down the known quantities
- Distance, r = 4.7 × 10-15 m
- The charge of one proton = +1.60 × 10-19 C
- An alpha particle (helium nucleus) has 2 protons
- So, charge of alpha particle, Q1 = 2 × 1.60 × 10-19 = +3.2 × 10-19 C
- The gold nucleus has 79 protons
- So, charge of gold nucleus, Q2 = 79 × 1.60 × 10-19 = +1.264 × 10-17 C
Step 2: Write down the equation for electric potential energy
Step 3: Substitute values into the equation
Exam Tip
This topic has a lot of confusing concepts and language. Make time to take notes on this topic and learn the correct equations for each quantity. When calculating electric potential energy, make sure you do not square the distance!