⚡ Electricity Calculators
Calculate Coulomb's law, electric field, capacitance, magnetic force, and explore the EM spectrum.
All Electricity Tools
What Is Electricity and Electromagnetism?
Electricity and magnetism are two aspects of a single fundamental force — electromagnetism. It governs how charged particles interact, how electric fields exert forces, how capacitors store energy, and how moving charges create magnetic effects. From the electrons powering your computer to the radio waves carrying Wi-Fi signals, electromagnetism is the physics of modern technology.
Core Electricity Formulas
Step-by-Step Example: Coulomb's Law
Two charges, q₁ = 2 μC and q₂ = 3 μC, are placed 0.1 m apart. What is the electrostatic force between them?
- Convert units: 2 μC = 2×10⁻⁶ C, 3 μC = 3×10⁻⁶ C
- Apply Coulomb's Law: F = k × q₁ × q₂ / r² = (8.99×10⁹) × (2×10⁻⁶) × (3×10⁻⁶) / (0.1)²
- Calculate: F = (8.99×10⁹ × 6×10⁻¹²) / 0.01 = 53.94 / 0.01 = 5.394 N
This is a repulsive force (both charges have the same sign) of about 5.4 N — roughly the weight of a 550 g object.
Step-by-Step Example: Capacitance
A capacitor stores 50 μC of charge at a voltage of 10 V. What is its capacitance?
- Apply C = Q / V: C = (50×10⁻⁶) / 10 = 5 μF (microfarads)
The Electromagnetic Spectrum
All electromagnetic radiation travels at the speed of light (c = 3×10⁸ m/s) but differs in frequency and wavelength. From lowest to highest frequency: radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays. The relationship is: c = f × λ, where f is frequency (Hz) and λ is wavelength (m).
Real-World Applications
- Electronics: Capacitors in circuits use C = Q/V to filter signals and store energy
- MRI Machines: Magnetic force on charged particles (F = qvB) underlies magnetic resonance imaging
- Particle Accelerators: Coulomb's Law governs how charged beams are steered and focused
- Telecommunications: Radio wave frequencies are calculated using f = c/λ
- Electric Motors: The magnetic force formula determines torque output in motors
Historical Context
Charles-Augustin de Coulomb quantified electrostatic force in 1785 using a torsion balance. Michael Faraday discovered electromagnetic induction in 1831, and James Clerk Maxwell unified electricity and magnetism into four elegant equations (1865), predicting that light itself is an electromagnetic wave. Heinrich Hertz experimentally confirmed radio waves in 1887, opening the age of wireless communication.
Frequently Asked Questions
What is the difference between electric force and electric field?
Electric force (F) is the actual force experienced by a specific charge q placed in the field: F = q × E. Electric field (E) is a property of space that describes how a unit positive test charge would be affected at that location. You calculate E first, then find the force on any charge by multiplying: F = qE.
What does capacitance measure?
Capacitance (measured in Farads, F) measures how much electric charge a capacitor can store per volt of potential difference. A 1 F capacitor stores 1 coulomb of charge per volt. Most practical capacitors are in the microfarad (μF) to picofarad (pF) range.
How does a magnetic force differ from an electric force?
An electric force acts on any charged particle regardless of motion. A magnetic force (F = qvB sinθ) only acts on moving charges and is always perpendicular to both the velocity and the magnetic field, meaning it changes the direction of motion but does no work on the particle.
What is Coulomb's constant?
Coulomb's constant k = 8.99 × 10⁹ N·m²/C² is derived from the permittivity of free space (ε₀): k = 1/(4πε₀). It determines the strength of the electrostatic force between two charges in vacuum.