# 18.2.3 Electric Potential Energy

### Electric Potential Energy of Two Point Charges

• The electric potential energy Ep at 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 Q1and Q2 is defined by: • Where:
• Ep = electric potential energy (J)
• r = separation of the charges Q1 and Q2 (m)
• ε0 = permittivity of free space (F m-1)
• The potential energy equation is defined by the work done in moving point charge Q2 from infinity towards a point charge Q1.
• The work done is equal to:

W = VQ

• Where:
• W = work done (J)
• V = electric potential due to a point charge (V)
• Q = Charge producing the potential (C)
• This equation is relevant to calculate the work done due on a charge in a uniform field
• Unlike the electric potential, the potential energy will always be positive
• Recall that at infinity, V = 0 therefore Ep = 0
• It is more useful to find the change in potential energy eg. as one charge moves away from another
• The change in potential energy from a charge Q1 at a distance r1 from the centre of charge Q2 to a distance r2 is equal to:

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

• Charge of alpha particle, Q1 = 2 × 1.60 × 10-19 = +3.2 × 10-19 C

The gold nucleus has 79 protons

• Charge of gold nucleus, Q2 = 79 × 1.60 × 10-19 = +1.264 × 10-17 C

#### Exam Tip

When calculating electric potential energy, make sure you do not square the distance! ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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