Electricity and Magnetism: Electrostatics, DC Circuits, Magnetic Fields, Electromagnetic Induction
This domain links three ideas: fields as descriptions of forces on charges, circuits as charge and energy bookkeeping, and induction as the coupling between changing magnetic flux and voltage. Abitur tasks often chain them - a coil in a changing field drives a current that deflects an electron beam.
Electrostatics
E = F/q; for a point charge E = (1/4πε₀)·q/r²; between plates E = U/d. Coulomb force F = (1/4πε₀)·q₁q₂/r². Voltage is energy per charge: W = q·U. Field lines run from plus to minus; equipotential surfaces are perpendicular to them.
DC circuits
Kirchhoff: ΣI = 0 at a node, ΣU = 0 around a loop. Series R = R₁ + R₂; parallel 1/R = Σ1/R_i. R = ρ·l/A. A real source obeys U_Kl = U₀ − I·R_i, so maximum power is delivered at R = R_i.
Magnetic fields
F = q·v·B·sin θ, perpendicular to both v and B (right-hand rule). A charge moving perpendicular to B follows a circle: r = mv/(qB). After acceleration through U, e/m = 2U/(B²r²) - the Fadenstrahlrohr result.
Induction
Φ = B·A·cos θ; U_ind = −N·dΦ/dt. Lenz's law fixes the direction: the induced current opposes the change in flux. A coil rotating with angular frequency ω gives U_ind = N·B·A·ω·sin(ωt).
Worked example
In a Fadenstrahlrohr electrons are accelerated through 250 V and enter B = 1.0 mT perpendicular to the field; the visible circle has r = 5.3 cm. From eU = ½mv² and r = mv/(eB): e/m = 2U/(B²r²) = 2·250/((1.0×10⁻³)²·(0.053)²) = 1.8×10¹¹ C/kg, against the accepted 1.76×10¹¹ C/kg - agreement within about 2 %, limited by reading the radius.
Traps
- Dropping the N turns in the induction law.
- Using the full B instead of the component perpendicular to the area.
- Predicting the Lenz direction by opposing the field rather than the change in flux.
- Ignoring internal resistance when calculating terminal voltage.
- Confusing technische Stromrichtung with the electron drift direction.