Static Electricity Formula – Formula, Derivation, Applications, Example Problems

What is Static Electricity Formula?

Static electricity refers to the electric charge that builds up on the surface of objects. The static electricity formula used to calculate the force between two charged objects due to static electricity is derived from Coulomb’s Law. This law was discovered by Charles-Augustin de Coulomb in 1785. It states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

The formula is expressed as:

• 𝐹 is the electrostatic force between the charges (in newtons, N).
• 𝑞₁ and 𝑞₂ are the amounts of the charges (in coulombs, C).
• 𝑟 is the distance between the charges (in meters, m).
• 𝑘 is Coulomb’s constant, approximately 8.987×109 N m²/C².

Derivation of Static Electricity Formula

Step 1: Establishing the Proportionality

First, we establish that the force 𝐹F between two point charges is proportional to the product of the magnitudes of the charges (𝑞1 and 𝑞2​) and inversely proportional to the square of the distance (𝑟r) between them:

Step 2: Introducing Coulomb’s Constant

To convert the proportionality into an equation, we introduce Coulomb’s constant 𝑘k, which has a value of approximately 8.987×1098.987×109 N·m²/C². This constant aligns the units and provides the correct scaling factor based on experimental evidence:

Applications of Static Electricity Formula

1. Electrostatic Precipitators: Industries use this technology to remove fine particles like dust and smoke from a flowing gas using the force exerted by a high-voltage electrostatic field.
2. Photocopiers and Laser Printers: These devices employ static electricity to attract toner particles to paper. The static charge holds the toner until it is permanently fused onto the paper.
3. Paint Spraying: Car manufacturers and other industries use electrostatic spray painting, which improves the efficiency of spray painting. The charged paint droplets attract to the oppositely charged object, minimizing waste.
4. Inkjet Printers: They manipulate tiny droplets of ink through electrostatic charges, precisely placing the ink on the paper as it passes through the printer.
5. Air Cleaners: Home and industrial air cleaners often incorporate static electricity to trap dust, pollen, and other airborne particles, improving air quality.
6. Material Separation: Electrostatic principles help in recycling processes, where different materials are separated based on their response to electric fields.

Example Problems on Static Electricity Formula

Example 1: Calculating Force between Two Charges

Problem: Two small spheres are charged with +3 microcoulombs and -5 microcoulombs respectively. They are 0.5 meters apart in a vacuum. Calculate the force between them using Coulomb’s Law.

Solution:

• Charge 𝑞1=+3×10⁻⁶ C
• Charge 𝑞2=−5×10⁻⁶ C
• Distance 𝑟=0.5 m
• Coulomb’s constant 𝑘=8.987×109 N m²/C²

Using the formula, 𝐹=𝑘 ( (∣𝑞₁×𝑞₂∣) / 𝑟²)

𝐹=8.987×10⁹× ( (∣3×10⁻⁶ × −5×10⁻⁶) / 0.5²)

​𝐹=8.987×10⁹ ×( (15×10⁻¹² ) / 0.25)

𝐹=8.987×10⁹×60×10⁻¹²

𝐹=539.22 N

The force is attractive since the charges are opposite.

Example 2: Distance Affecting Force

Problem: What is the Electrostatic force between two charged objects with charges of +10 Microcoulombs each, placed 2 meters apart?

Solution:

• Charge 𝑞1=+10×10⁻⁶ C
• Charge 𝑞2=+10×10⁻⁶ C
• Distance 𝑟=2 m
• Coulomb’s constant 𝑘=8.987×109 N m²/C²

Using the formula, 𝐹=𝑘( (∣𝑞₁×𝑞₂∣) / 𝑟²)

𝐹=8.987×10⁹×( ((10×10⁻⁶)×(10×10⁻⁶)) / 2² )

𝐹=8.987×10⁹×( (100×10⁻¹²) / 4)

𝐹=8.987×10⁹×25×10⁻¹²

𝐹=224.675 N

The force is repulsive as both charges are positive.

Example 3: Variable Charge and Distance

Problem: Calculate the force exerted between a charge of +2 Microcoulombs and another charge of +6 Microcoulombs, separated by a distance of 3 meters.

Solution:

• Charge 𝑞1=+2×10⁻⁶ C
• Charge 𝑞2=+6×10⁻⁶ C
• Distance 𝑟=3 m
• Coulomb’s constant 𝑘=8.987×109 N m²/C²

Using the formula, 𝐹=𝑘 ( (∣𝑞₁×𝑞₂∣) / 𝑟²)

𝐹=8.987×10⁹ × ( (2×10⁻⁶×6×10⁻⁶) / 3²)

𝐹=8.987×10⁹ × ((12×10⁻¹²) / 9))

​𝐹=8.987×10⁹ × 1.333×10⁻¹²

𝐹=11.983 N

The force is also repulsive, with both charges being positive.

FAQs

How to Calculate Static Energy

Static energy can’t calculated. We can calculate static force using Coulomb’s Law​​.

What is Electrostatic Equation?

The electrostatic equation refers to Coulomb’s Law: 𝐹= (1/4πε0) x (∣𝑞₁×𝑞₂∣ / 𝑟²), which calculates the force between two charges.

At What Voltage Can You Feel Static Electricity?

You can feel static electricity at voltages as low as 3,000 volts, typical in everyday static discharges.