> ## Documentation Index
> Fetch the complete documentation index at: https://otzr-mintlify-3a69404b.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.
# Electricity and Magnetism
> The invisible forces that run your phone, your car, and even your nervous system.
## Where it all starts: charge
Everything is made of atoms. Atoms have:
* **Protons** — positive charge (+)
* **Electrons** — negative charge (−)
* **Neutrons** — no charge (neutral)
Opposite charges *pull* on each other. Same charges *push* each other away. That's the entire foundation of electricity and magnetism.
When you rub a balloon on your hair and it sticks to the wall, you transferred a few electrons from your hair to the balloon. The balloon is slightly negative, the wall is slightly more positive in response — and they attract. That's it. That's static electricity.
## Current: charges on the move
> **Electric current is the flow of electrons through a wire.**
Measured in **amperes (A)** — one amp = a huge number of electrons (about 6 × 10¹⁸) passing a point each second.
Think of a wire like a hose:
* **Current (A)** = how much water flows per second.
* **Voltage (V)** = the pressure pushing the water.
* **Resistance (Ω, ohms)** = how narrow or clogged the hose is.
This water analogy is rough but powerful. Most electrical intuition comes from it.
## Ohm's Law: the one equation you need
$V = IR$
Voltage = Current × Resistance.
Read it three ways:
* More voltage → more current (push harder, more flow).
* More resistance → less current (clog the hose, less flow).
* Want to know voltage? Multiply current by resistance.
With this single equation, you can analyze 90% of basic circuits.
### Example
A light bulb has 240 Ω of resistance and you plug it into 120 V.
$I = \frac{V}{R} = \frac{120}{240} = 0.5 \text{ A}$
Half an amp of current. From one tiny equation.
## Power: how fast the energy is used
For electric circuits, power is even simpler:
$P = V \cdot I$
That 120 V bulb at 0.5 A:
$P = 120 \times 0.5 = 60 \text{ W}$
A 60-watt bulb. The number on the package matches the math. Beautiful.
This is why high voltage is used to transmit electricity over long distances — you can move the same power with much less current, which means much less wasted heat in the wires.
## Circuits: two layouts that explain everything
Components in a line. Same current goes through each one. Add resistances together.
*One bulb burns out and the whole string dies.* (Old Christmas lights.)
Components on separate branches. Each gets the full voltage. Currents add up.
*One bulb burns out, the rest stay on.* (Your house wiring.)
Every circuit on Earth is some combo of these two patterns. That's it.
## Magnetism: the same thing, in disguise
Here's the wild secret that took 200 years to figure out: **electricity and magnetism are the same force, seen from different angles.**
The rules:
A current flowing through a wire creates a magnetic field around it. Wrap the wire in a coil and the field gets strong — that's an **electromagnet**. This is how motors, MRI machines, and electric door locks work.
Move a magnet near a coil of wire and electricity flows in the wire. *Without* touching anything. This is called **electromagnetic induction**, and it's how every generator on the planet makes electricity — wind, hydro, coal, nuclear, all of them spin a magnet near coils.
A wiggling electric field makes a wiggling magnetic field, which makes a wiggling electric field, and so on — a self-sustaining wave that travels at the speed of light. That **is** light. Light is the wave that electricity and magnetism make together.
This is why your phone works. Radio waves, Wi-Fi, Bluetooth, 5G — they're all the same kind of wave, just at different frequencies. Higher frequency: visible light. Even higher: X-rays. Lower than radio: nothing useful, but it's all the same phenomenon.
## A motor in one paragraph
Put a coil of wire between two magnets. Run current through the coil. The current creates its own magnetic field, which fights the magnets' field. To resolve the fight, the coil spins. **Spinning coil = motor.** Every fan, drill, electric car, and washing machine is some version of this trick.
Reverse it: spin the coil with an external force (wind, water, steam) instead of giving it current. The spinning coil in the magnetic field *generates* a current. **Spinning coil = generator.** Every power plant on Earth.
Motor and generator are the same machine, run in opposite directions. That symmetry is one of the most beautiful things in engineering.
## AC vs. DC: the two flavors of electricity
Electrons flow steadily one direction. **Batteries, USB, electronics.**
Electrons swing back and forth 50 or 60 times a second. **Wall outlets, the power grid.**
We use AC for the grid because it's *very* easy to step voltage up and down with transformers — which lets us send power across long distances efficiently. Your phone charger then converts that AC back into DC for the battery.
## Why this matters to a mechanical engineer
Electricity and magnetism are how mechanical force becomes electrical signals (sensors), and how electrical signals become mechanical motion (motors, solenoids, actuators). Pretty much every modern machine is part-mechanical, part-electromagnetic. If you understand both sides, you can build almost anything.
How an engineer actually attacks a physics problem from scratch.