Field lines of point charges
Two charges and the field rearranges itself. A test charge measures where the force is strongest.
Physics – grade 12
Qualification phase Q1 “Electric and magnetic field” and Q2 “Oscillations, induction and mechanical waves”. Q1.1–Q1.2 and Q2.1–Q2.3 are mandatory. Assigning them to grade 12 is an assumption (G9). “Advanced course only” marks the higher level.
Unit Q1.1Electric field
Mandatory topic area. Field concept, field-line patterns and field strength, capacitor as energy store with charging and discharging, Coulomb's law and motion of charged particles in the field.
Q1.1.1Concept of a field using electric fields
Field-line patterns (parallel plates, point charge, dipole), charge conservation and induction of charge.
Q1.1.2Electric field strength
Defining field strength; radial field; graphical superposition.
Field lines of point charges
Two charges and the field rearranges itself. A test charge measures where the force is strongest.
Q1.1.3Capacitor as energy store: electric field, capacitance, electrical energy
Capacitance, field energy and time behaviour during charging and discharging.
Charging and discharging a capacitor
A capacitor charges through a resistor and discharges again. The graphs show how voltage and current change over time.
Q1.1.4Coulomb's law
Force between point charges.
No separate simulation is planned for this.
Q1.1.5Forces on bodies in uniform electric fields, trajectories (qualitative), energy considerations
Millikan experiment, acceleration of charged particles and deflection across the field.
No separate simulation is planned for this.
Q1.1.6Concept of a field using electric fields (advanced course only)
Surface charge density and quantitative superposition of fields.
Field lines of point charges
Two charges and the field rearranges itself. A test charge measures where the force is strongest.
Q1.1.7Capacitor as energy store: electric field, capacitance, electrical energy (advanced course only)
Dielectric, derivations and differential equation of discharge.
Charging and discharging a capacitor
A capacitor charges through a resistor and discharges again. The graphs show how voltage and current change over time.
Q1.1.8Voltage as potential difference (advanced course only)
Electric potential and equipotential lines.
No separate simulation is planned for this.
Q1.1.9Forces on bodies in uniform electric fields, trajectories, energy considerations (advanced course only)
Quantitative deflection (comparison with horizontal projectile), linear accelerator.
No separate simulation is planned for this.
Unit Q1.2Magnetic field
Mandatory topic area. Magnetic field-line patterns and flux density, field of a long solenoid, and Lorentz force and circular paths of charged particles (fine-beam tube, e/m).
Q1.2.1Concept of a field using magnetic fields
Field lines of permanent magnet, straight wire and solenoid.
No separate simulation is planned for this.
Q1.2.2Magnetic flux density
Defining flux density and determining it inside a long solenoid.
No separate simulation is planned for this.
Q1.2.3Forces on bodies in uniform magnetic fields, trajectories (qualitative)
Lorentz force as centripetal force and circular path in the fine-beam tube.
Lorentz force and fine-beam tube
Electrons fly along a glowing circular path in a magnetic field. From the radius you determine a property of the electron.
Q1.2.4Quantitative treatment of trajectories in uniform fields (advanced course only)
Crossed fields and velocity filter.
Lorentz force and fine-beam tube
Electrons fly along a glowing circular path in a magnetic field. From the radius you determine a property of the electron.
Q1.2.5Hall effect (advanced course only)
Explaining the voltage across a conductor in a magnetic field.
No separate simulation is planned for this.
Q1.2.6Particle accelerators (advanced course only)
Working principle of e.g. cyclotron and synchrotron.
No separate simulation is planned for this.
Unit Q2.1Mechanical oscillations
Mandatory topic area. Harmonic oscillations of spring and simple pendulums with their parameters, equation of motion, energy conversion and damping; in the advanced course forced oscillations and resonance.
Q2.1.1Mechanical harmonic oscillations: characteristic quantities and their relationships
Displacement, amplitude, period, frequency and energy (qualitative).
Spring pendulum
A mass bounces up and down on a spring. Graphs show position, speed and energy during the oscillation.
Simple pendulum
Pull a pendulum aside, let it go and measure how long one swing takes. What does it depend on? Also with large angles and damping.
Q2.1.2Time course of a harmonic oscillation
Linear restoring force, period of spring and simple pendulum, equation of motion.
Spring pendulum
A mass bounces up and down on a spring. Graphs show position, speed and energy during the oscillation.
Simple pendulum
Pull a pendulum aside, let it go and measure how long one swing takes. What does it depend on? Also with large angles and damping.
Q2.1.3Damped mechanical oscillations
Describing the decrease in amplitude qualitatively.
No separate simulation is planned for this.
Q2.1.4Time course of a harmonic oscillation (advanced course only)
Differential equation of undamped oscillation with trial solution.
Spring pendulum
A mass bounces up and down on a spring. Graphs show position, speed and energy during the oscillation.
Q2.1.5Damped oscillations (advanced course only)
Describing damping behaviour (without derivation).
No separate simulation is planned for this.
Q2.1.6Forced oscillations (advanced course only)
Natural frequency, resonance, resonance curves and resonance disaster.
Driven oscillation and resonance
A motor drives an oscillating wheel. If the motor hits exactly the right rhythm, the wheel swings especially strongly: resonance.
Unit Q2.2Induction and electromagnetic oscillations
Mandatory topic area. Induction through change of magnetic flux, Lenz's law, self-induction and the electromagnetic oscillating circuit.
Q2.2.1Induction due to a change of magnetic flux over time
Magnetic flux and law of induction with average rate of change.
Electromagnetic induction
Magnet in, the needle swings. Magnet out, it swings the other way. Every generator works on the same principle.
Q2.2.2Relationship between the direction of the induced current and its effect (Lenz's law)
Justifying the direction of the induced current.
Electromagnetic induction
Magnet in, the needle swings. Magnet out, it swings the other way. Every generator works on the same principle.
Q2.2.3Self-induction and inductance of a long solenoid (phenomenological)
Observing and describing self-induction in coils.
No separate simulation is planned for this.
Q2.2.4Example of a technical application of induction
Explaining e.g. a generator or transformer.
No separate simulation is planned for this.
Q2.2.5Electromagnetic harmonic oscillations
LC circuit: parameters, energy conversion, Thomson's formula.
No separate simulation is planned for this.
Q2.2.6Induction due to a change of magnetic flux over time (advanced course only)
Law of induction in differential form, including non-linear cases.
Electromagnetic induction
Magnet in, the needle swings. Magnet out, it swings the other way. Every generator works on the same principle.
Q2.2.7Self-induction and inductance (advanced course only)
Switch-on and switch-off processes, definition of inductance.
No separate simulation is planned for this.
Q2.2.8Energy of the field of a current-carrying coil (advanced course only)
Magnetic field energy (without derivation).
No separate simulation is planned for this.
Q2.2.9Comparison of mechanical and electromagnetic oscillations in terms of energy (advanced course only)
Analogies between pendulum and LC circuit.
No separate simulation is planned for this.
Q2.2.10Damped oscillations (advanced course only)
Damping in the LC circuit.
No separate simulation is planned for this.
Q2.2.11Forced oscillations, resonance (qualitative) (advanced course only)
Resonance in the electromagnetic circuit.
Driven oscillation and resonance
A motor drives an oscillating wheel. If the motor hits exactly the right rhythm, the wheel swings especially strongly: resonance.
Unit Q2.3Mechanical waves
Mandatory topic area. Formation and parameters of harmonic waves, longitudinal and transverse waves, typical wave phenomena, interference and standing waves.
Q2.3.1Harmonic waves: characteristic quantities and their relationships
Generation, propagation, wavelength, frequency and c = λ·f.
Transverse and longitudinal waves
A wave travels through a chain of particles. Each particle only oscillates in place, across or along the direction of travel.
Q2.3.2Definition of a harmonic wave as a process periodic in space and time
Representation in t-y and x-y diagrams, longitudinal and transverse waves, polarisation.
Transverse and longitudinal waves
A wave travels through a chain of particles. Each particle only oscillates in place, across or along the direction of travel.
Q2.3.3Refraction, reflection, diffraction as characteristic wave phenomena
Wave phenomena e.g. in a ripple tank; Huygens' principle.
No separate simulation is planned for this.
Q2.3.4Superposition of waves
Interference of two sources, path difference, positions of maxima and minima.
Interference of two circular waves
Two circular waves overlap: in some places they reinforce each other, in others they cancel out.
Q2.3.5Standing waves
One-dimensional standing waves and determining the wavelength.
Standing waves
A wave is reflected at the end and a fixed pattern of nodes and antinodes appears, like on a guitar string.
Q2.3.6Harmonic waves: characteristic quantities and their relationships (advanced course only)
Wave equation for development in space and time.
Transverse and longitudinal waves
A wave travels through a chain of particles. Each particle only oscillates in place, across or along the direction of travel.
Q2.3.7Phase jump on reflection, fixed and free end for standing waves (advanced course only)
Reflection at fixed and free ends.
Standing waves
A wave is reflected at the end and a fixed pattern of nodes and antinodes appears, like on a guitar string.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Kerncurriculum, Gymnasium, Physics, grade 12