Size of Force Between Two Static Electric Charges Revision Notes for Leaving Cert Physics

Size of Force Between Two Static Electric Charges

Introduction to forces between static charges

When two static electric charges are brought near each other, they will experience a force. This force can either push the charges apart (repulsion) or pull them together (attraction), depending on the types of charges involved. Understanding how to calculate the magnitude of this force is fundamental to studying electrostatics.

The force that one static charge exerts on another depends on several key factors that we need to consider when making calculations.

Factors affecting the force magnitude

The strength of the electrostatic force between two charges is determined by three main factors:

The size of each charge - Larger charges produce stronger forces
The distance between the charges - Greater separation leads to weaker forces
The material surrounding the charges - Different media can strengthen or weaken the force

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These relationships mean that doubling the size of either charge will double the force, whilst doubling the distance between charges will reduce the force to one-quarter of its original value.

Coulomb's law

The mathematical relationship governing the force between static charges is known as Coulomb's law. This fundamental principle is essential for all electrostatic calculations.

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Coulomb's Law states: The electrostatic force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's law can be written as:

$F = k \frac{q\_1 q\_2}{d^2}$

Where:

F = force between the charges (in Newtons)
q₁ and q₂ = the two electric charges (in Coulombs)
d = distance between the charge centres (in metres)
k = a constant depending on the surrounding medium

For charges in air or a vacuum, the formula becomes:

$F = \frac{1}{4\pi\varepsilon\_0} \frac{q\_1 q\_2}{d^2}$

Where ε₀ is the permittivity of free space, and k = 8.9 × 10⁻⁹ F⁻¹m⁻¹.

Understanding the inverse square law

Coulomb's law is an example of an inverse square law, which means the force decreases with the square of the distance. This relationship has important practical consequences:

If the distance is doubled, the force becomes four times smaller
If the distance is tripled, the force becomes nine times smaller
If the distance is halved, the force becomes four times larger

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This inverse square relationship explains why electric forces become very weak over large distances but can be extremely strong when charges are close together.

Effect of the surrounding medium

The medium surrounding the electric charges affects the force between them. This effect is described by the permittivity of the material, represented by the symbol ε.

In a vacuum, the permittivity has its lowest value (ε₀)
In air, the permittivity is approximately the same as in vacuum
In other materials, the permittivity is usually higher, which reduces the force between charges

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The permittivity appears in the denominator of Coulomb's law, so materials with higher permittivity produce weaker electrostatic forces.

Worked examples

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Worked Example 1: Basic Force Calculation

Calculate the force between a +5 C charge and a +6 C charge separated by 4 m in air.

Solution: Using Coulomb's law: $F = k \frac{q\_1 q\_2}{d^2}$

$F = (8.9 \times 10^{-9}) \frac{(5)(6)}{4^2}$

$F = (8.9 \times 10^{-9}) \frac{30}{16}$

$F = 1.68 \times 10^{-8}$ N

Since both charges are positive, the force is repulsive.

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Worked Example 2: Force with Opposite Charges

Two point charges of +2 μC and -3 μC are 50 cm apart in air. Find the magnitude and direction of the force.

Solution: First, convert units: 2 μC = 2 × 10⁻⁶ C, -3 μC = -3 × 10⁻⁶ C, 50 cm = 0.5 m

$F = (8.9 \times 10^{-9}) \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.5)^2}$

$F = (8.9 \times 10^{-9}) \frac{6 \times 10^{-12}}{0.25}$

$F = 2.136 \times 10^{-19}$ N

Since the charges have opposite signs, the force is attractive.

Important notes about electric forces

Several key principles apply to all electrostatic force situations:

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Newton's Third Law: Each charge experiences the same magnitude of force, but in opposite directions.

Force Direction: The force always acts along the line joining the two charges.

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Charge Interactions:

Like charges repel - charges with the same sign push each other away
Unlike charges attract - charges with opposite signs pull towards each other
Point charge assumption - Coulomb's law applies exactly only to point charges, but gives good approximations for small charged objects when the separation is large compared to their size

The magnitude of the force is always the same on both charges, regardless of their individual sizes, following Newton's third law of motion.

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Key Points to Remember:

Coulomb's law: $F = k \frac{q\_1 q\_2}{d^2}$ describes the force between static charges
The force depends on the product of the charges and inversely on the square of their separation
Doubling the distance reduces the force to one-quarter of its original value
Like charges repel each other while opposite charges attract
The surrounding medium affects the force strength through its permittivity

Size of Force Between Two Static Electric Charges (Leaving Cert Physics): Revision Notes