Magnetism and Electromagnetic Induction
Describe magnetic fields, forces on moving charges and currents, motors, generators, transformers, and electromagnetic induction conceptually.
A lesson of Physics, in Electricity and Magnetism, about 10 minutes.
By the end of this lesson, you will be able to describe magnetic fields and forces, explain how moving charges create magnetic fields, and apply Faraday's Law of electromagnetic induction.
Magnetic Fields
Magnetic field ($\vec{B}$): a vector field that exerts forces on moving charges and magnetic materials.
Units: Tesla (T) = kg/(A·s²).
Magnetic field lines: form closed loops from N to S poles externally (and S to N inside the magnet); unlike electric field lines, they never start or stop.
Earth's magnetic field: North geographic pole ≈ South magnetic pole (~0.5 × 10⁻⁴ T).
Force on a Moving Charge
$$\vec{F} = q\vec{v} \times \vec{B}$$
Magnitude: $F = qvB\sin\theta$
Right-hand rule: point fingers in direction of $\vec{v}$; curl toward $\vec{B}$; thumb points in direction of $\vec{F}$ (for positive charge).
Key: the magnetic force is always perpendicular to velocity → changes direction but not speed → circular motion in a uniform field.
Magnetic Force on a Wire
$$\vec{F} = I\vec{L} \times \vec{B}$$
Magnitude: $F = BIL\sin\theta$
Example: two parallel wires carrying currents in the same direction attract each other; opposite directions → repel.
Magnetic Field from a Current
Straight wire: $B = \frac{\mu_0 I}{2\pi r}$ ($\mu_0 = 4\pi \times 10^{-7}$ T·m/A)
Solenoid: $B = \mu_0 nI$ ($n$ = turns per unit length)
Electromagnetic Induction (Faraday's Law)
A changing magnetic flux induces an EMF.
$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$
$\Phi_B = BA\cos\theta$ (magnetic flux)
Lenz's Law: the induced current opposes the change in flux that created it (minus sign in Faraday's Law).
Applications
Generator: rotating coil in magnetic field → changing flux → AC voltage.
Transformer: changing current in primary coil → changing flux → EMF in secondary coil.
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
Inductive charging, wireless power transfer, MRI machines — all rely on electromagnetic induction.
Summary
Magnetic force on charge: $F = qvB\sin\theta$; perpendicular to motion → circular path.
Faraday's Law: changing $\Phi_B$ → induced EMF; Lenz's Law determines direction.
voltage ratio = turns ratio; changes voltage while conserving power.