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

Series

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.)

Parallel

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:

1. Moving charges create magnetic fields

   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.

2. Changing magnetic fields create electric currents

   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.

3. This back-and-forth makes light

   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

Direct Current (DC)

Electrons flow steadily one direction. Batteries, USB, electronics.

Alternating Current (AC)

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.

Next: Problem-Solving Toolkit

How an engineer actually attacks a physics problem from scratch.