Magnetism & Electromagnetism Cheat Sheet

A printable reference covering magnetic fields, forces, flux, induction, solenoids, transformers, and right-hand rules for grades 10-12.

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Magnetism and electromagnetism connect electric current, magnetic fields, forces, and energy transfer. This cheat sheet helps students organize the main equations used in force, field, flux, induction, motor, and transformer problems. It is useful for quickly checking which angle, direction rule, and unit belong with each formula. Students in grades 10-12 need these relationships for circuits, motion in fields, generators, and electromagnetic induction.

Key Facts

The magnetic force on a moving charge is $F = qvB\sin\theta$ , where $\theta$ is the angle between the velocity $\vec{v}$ and magnetic field $\vec{B}$ .
The magnetic force on a current-carrying wire is $F = ILB\sin\theta$ , where $L$ is the length of wire inside the magnetic field.
The magnetic field around a long straight wire is $B = \frac{\mu_0 I}{2\pi r}$ , where $r$ is the distance from the wire.
The magnetic field inside a long solenoid is approximately $B = \mu_0 nI$ , where $n = \frac{N}{L}$ is the number of turns per meter.
Magnetic flux through a flat loop is $\Phi_B = BA\cos\theta$ , where $\theta$ is measured between $\vec{B}$ and the area vector perpendicular to the loop.
Faraday's law gives induced emf as $\mathcal{E} = -N\frac{\Delta \Phi_B}{\Delta t}$ , and the negative sign shows the direction described by Lenz's law.
The torque on a rectangular current loop in a uniform magnetic field is $\tau = NIAB\sin\theta$ .
For an ideal transformer, $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ and $\frac{I_s}{I_p} = \frac{N_p}{N_s}$ .

Vocabulary

Magnetic field: A magnetic field is a region where moving charges, currents, or magnetic materials experience magnetic forces, represented by the vector $\vec{B}$ .
Magnetic flux: Magnetic flux $\Phi_B$ measures how much magnetic field passes through an area, calculated with $\Phi_B = BA\cos\theta$ for a uniform field.
Electromagnetic induction: Electromagnetic induction is the production of an emf or current when the magnetic flux through a circuit changes.
Lorentz force: The Lorentz force is the total electromagnetic force on a charge, written as $\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}$ .
Solenoid: A solenoid is a coil of wire that creates a strong, nearly uniform magnetic field inside when current flows through it.
Lenz's law: Lenz's law states that an induced current flows in the direction that opposes the change in magnetic flux that caused it.

Common Mistakes to Avoid

Using $\cos\theta$ instead of $\sin\theta$ for magnetic force is wrong because $F = qvB\sin\theta$ and $F = ILB\sin\theta$ depend on the component perpendicular to the magnetic field.
Measuring the flux angle from the surface of the loop is wrong because $\Phi_B = BA\cos\theta$ uses the angle between $\vec{B}$ and the area vector, which is perpendicular to the surface.
Ignoring the negative sign in $\mathcal{E} = -N\frac{\Delta \Phi_B}{\Delta t}$ is wrong because it represents Lenz's law and determines the direction of the induced current.
Applying $B = \frac{\mu_0 I}{2\pi r}$ inside a solenoid is wrong because that formula is for a long straight wire, while a long solenoid uses $B = \mu_0 nI$ .
Reversing transformer ratios is wrong because voltage follows turns with $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ , while current follows the inverse ratio in an ideal transformer.

Practice Questions

1 A charge of $q = 3.0 \times 10^{-6}\,\text{C}$ moves at $v = 4.0 \times 10^5\,\text{m/s}$ perpendicular to a magnetic field of $B = 0.20\,\text{T}$ . Find the magnetic force magnitude.
2 A wire of length $L = 0.50\,\text{m}$ carries current $I = 6.0\,\text{A}$ at $90^\circ$ to a magnetic field of $B = 0.30\,\text{T}$ . Calculate the force on the wire.
3 A coil has $N = 200$ turns and its magnetic flux changes from $0.060\,\text{Wb}$ to $0.015\,\text{Wb}$ in $0.25\,\text{s}$ . Find the magnitude of the induced emf.
4 A loop is pulled out of a region with a uniform magnetic field. Explain how Lenz's law predicts the direction of the induced current and why the induced field opposes the change.