The Italian delegation of Science on Stage 2

Let's prove the fourth Maxwell equation

Abstract

Teaching electro-magnetism is someway not easy. Even if today it's possible to realise many experiments that prove a lot of laws, it's difficult to show that a time-varying electric field generates a magnetic field. We want to fill this hole by realising a cheap device that highlights this phenomena. The core of the system is a big capacitor with two circular plates separated by a polystirene dielectric. By applying a medium frequency sinusoidal voltage, we compare the magnetic field near the dielectric with the magnetic field generated by the current flowing through the conductors connected to the capacitor (at the same distance by the axis of the system) showing that its amplitude does not vary, according to the displacement current concept. For understanding the experiment it is necessary to know other electromagnetic phenomena (i.e. Biot-Savart and Faraday induction laws) that are reminded by a preliminary set of classical experiments. This lab activities were proposed to the students of a secondary school. The tests submitted to the students highlighted a well understanding of the displacement current concept.

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Description

Electromagnetism teaching is supported by a lot of experiments. Anyway, it is difficult to show that a time-varying electric field generates a magnetic field.

Goals

• To realize an experiment that highlights that a variable electric field generates a magnetic field;
• to introduce this experiment with a brief propaedeuti-cal set of tests aimed at showing more common electric and magnetic phenomena.

The propaedeutical set of experiments

• The magnetic effects of a direct current:
  • a compass needle detects the field;
  • no induction phenomena are involved on a coil.
• The magnetic effects of a time-varying current (by transients): a coil detects voltage.
• The magnetic effects of a sinusoidal current: the induced voltage on a coil is proportional to the maximum amplitude and the frequency of the current.

The effects of a time-varying electric field

We have realized a cylindrical symmetric structure aimed at showing:

• that the magnetic field in proximity of a plane con denser crossed by a displacement current I(t) is equal to the field generated by the same conduction current that crosses a vertical segment.
• That the magnetic field is weaker if the capacitor is replaced by a shunt that emulates the absence of magnetic field from the dielectric.