# 7.3 Electric Force between Two Charges

## Electric Force between Two Charges

• All charged particles produce an electric field around them
• This field exerts a force on any other charged particle within range

• The electrostatic force between two charges is defined by Coulomb’s Law
• Recall that the charge of a uniform spherical conductor can be considered as a point charge at its centre

• Coulomb’s Law states that:

The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation

• The force FE between two charges as expressed by Coulomb's Law is given by the equation:

The electrostatic force between two charges is defined by Coulomb’s Law

• Where:
• FE = electrostatic force between two charges (N)
• Q1 and Q2 = two point charges (C)
• ε0 = permittivity of free space
• r = distance between the centre of the charges (m)
• The 1/r2 relation is called the inverse square law
• This means that when the separation of two charges doubles, the electrostatic force between them reduces to (½)2 = ¼ of its original size
• ε0 is a physical constant used to show the capability of a vacuum to permit electric fields

• If Q1 and Q2 are oppositely charged, then the electrostatic force FE is negative
• This can be interpreted as an attractive force between Q1 and Q2

• If Q1 and Q2 are the same charge, then the electrostatic force FE is positive
• This can be interpreted as a repulsive force between Q1 and Q2

#### Worked example

An alpha particle is situated 2.0 mm away from a gold nucleus in a vacuum. Assuming they are point charges, calculate the magnitude of the force acting on each of the charges.

Atomic number of helium = 2

Atomic number of gold = 79

Charge of an electron = 1.60 × 10-19 C

Step 1: Write down the known quantities

• Distance, r = 2.0 mm = 2.0 × 10-3 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

Step 2: The electrostatic force between two point charges is given by Coulomb’s Law

Step 3: Substitute values into Coulomb's Law

#### Exam Tip

Remember to always square the distance, r between the charges!

Always look out for unit prefixes when substituting values into an equation. Check whether the charge has been converted into C instead of nC or µC, or the distance in mm to m to get a force F of newtons, N.

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