Electromagnetism: fields, forces and modern applications

Electromagnetism describes how electric charge, electric field, magnetic field and electromagnetic waves are linked. It is a pillar of modern physics and the basis of today's electrical technology.

Here you find superconductivity (Meissner effect, levitation) and a PEM fuel cell: how H₂ and O₂ produce current through charge separation and electron flow in the external circuit.

Superconductivity and the Meissner effect

Here you can see electromagnetism directly: magnetic field, levitation and transition to the normal state when temperature exceeds T_c.

Superconductivity and Meissner simulator screenshot

Formulas and explanations

Superconductivity condition

T < T_{c}

Below the critical temperature T_c the material becomes superconducting and magnetic field screening appears.

Magnetic force (educational model)

F_{m} \propto \frac{B^{2}}{h^{2}}

In the simulator the repulsive effect grows with the square of magnetic field B and decreases as distance h increases.

Vertical balance

F_{m} - m g = m a_{y}

Stable levitation occurs when magnetic force balances weight (F_m ≈ mg).

London penetration depth

λ_{L} = \sqrt{\frac{m}{μ_{0} n_{s} e^{2}}}

Describes the scale over which the magnetic field penetrates the superconductor before being screened.

PEM fuel cell

A proton-exchange membrane cell converts the chemical energy of hydrogen and oxygen into electric current: at the anode H₂ is oxidised, electrons travel through the external circuit, and H⁺ crosses the membrane to the cathode where O₂ is reduced and water forms.

Formulas and explanations

Overall reaction (educative model)

2 H_{2} + O_{2} \to 2 H_{2} O + energie

Chemical balance of the hydrogen cell: hydrogen and oxygen are consumed, water is produced, and part of the released energy appears as electrical work in the circuit.

Electrical power delivered to the load

P = U I

Useful power at the terminals is the product of voltage U and current I. In the simulator, higher flows or lower bulb resistance increase I and thus P.

Ohm's law (simple load)

I \approx \frac{U}{R}

For a resistive load R, current is tied to available voltage. The teaching model also limits current by reactant flow.

Efficiency (working definition)

η \approx \frac{P_{electric}}{P_{chimic disponibil}}

Efficiency compares electrical power output to power available from the chemical flow of reactants. H₂/O₂ imbalance or internal losses reduce η.