Magnetism and Electromagnetic Induction
Students investigate magnetic fields and explain how changing magnetic flux enables motors, generators, transformers, and power transmission.
Illustrations are auto-generated and may be placeholders. They can be refreshed to match the narration.
Magnetic Fields and Forces
A magnetic field is a vector field produced by magnets, moving charges, and electric currents. At each point, the field vector B gives the direction a north compass pole would point. Outside a bar magnet, field lines run from the north pole to the south pole; closer line spacing represents greater field magnitude. Around a long straight wire, the lines form concentric circles, with direction found by the right-hand rule: point your thumb with conventional current and curl your fingers. Two parallel current-carrying wires exert forces on one another. Currents in the same direction attract, while opposite currents repel. In an investigation, students can hold current and wire length constant, vary the separation, and measure force. A graph can model the inverse relationship F/L = μ₀I₁I₂/(2πr). For example, doubling the wire separation cuts the force per unit length in half.
Forces on Moving Charges
A charged particle moving through a magnetic field experiences the magnetic force F = qv × B, with magnitude F = |q|vB sin θ. The force is perpendicular to both the velocity and the magnetic field, so it changes the particle’s direction but does no work and does not change its speed. A positive charge follows the right-hand rule; a negative charge is forced in the opposite direction. If velocity is perpendicular to a uniform field, the force acts as a centripetal force and produces circular motion with radius r = mv/(|q|B). For example, a proton moving right through a field directed into the page curves upward. Increasing its speed increases the radius, while increasing the magnetic field decreases the radius. Particle accelerators and mass spectrometers use this predictable deflection to guide particles or identify ions by their mass-to-charge ratios.
Electromagnets and Motors
An electromagnet uses electric current to produce a controllable magnetic field. In a solenoid, many loops of wire create a nearly uniform internal field directed along the coil’s axis. Increasing the current, adding turns per unit length, or inserting a ferromagnetic core strengthens the field. Electric motors use the force on current-carrying wires, described by F = IL × B. In a rectangular coil, opposite sides experience forces in opposite directions, producing torque. For a coil with N turns, maximum area A, and angle θ, the torque magnitude is τ = NIAB sin θ. In a simple direct-current motor, a split-ring commutator reverses the coil’s current every half-turn so the torque continues in the same rotational direction. For example, the motor in a battery-powered fan converts electrical energy into the rotational kinetic energy of the blades, with some energy transferred as heat and sound.
Faraday's Law
Magnetic flux measures how much magnetic field passes through a surface. For a uniform field and flat loop, ΦB = BA cos θ, where θ is the angle between B and the loop’s area vector. Faraday’s law states that the induced emf is ε = -NΔΦB/Δt. Therefore, current is generated only when flux changes, such as when field strength, loop area, or orientation changes. The negative sign expresses Lenz’s law: the induced current creates a magnetic field that opposes the change in flux, conserving energy. For example, pushing a magnet’s north pole toward a coil increases flux; the coil’s near face becomes a north pole and repels the approaching magnet. Pulling the magnet away reverses the current. Students can move the magnet at different speeds, record peak voltage, and model peak emf as an approximately linear function of the rate of flux change.
Generators and Transformers
Generators convert mechanical energy to electrical energy by rotating a coil in a magnetic field. For steady rotation, the flux ΦB = BA cos(ωt) changes sinusoidally, so the induced emf also alternates. A transformer changes AC voltage using two coils around a shared iron core. Ideally, Vs/Vp = Ns/Np and Is/Ip = Np/Ns, while input and output power are approximately equal. A step-up transformer raises voltage and lowers current. Because line heating is Ploss = I²R, high-voltage, low-current transmission greatly reduces energy loss. For example, a power plant steps generator voltage up for long-distance lines, and substations step it down before local distribution. Infrastructure policy must balance efficiency, cost, reliability, land use, environmental justice, and exposure to hazards. Students can compare proposals for new transmission lines or transformer upgrades, use evidence about these tradeoffs, and explain which public policy best serves communities.