ElectroMagnetism

Introduction

A Brief History of Electromagnetism

While electricity and magnetism were known as separate forces, 19th-century discoveries lead scientists to the first unification in physics, the unification of electricity and magnetism.

1820, Oersted and Ampere

In 1820, physicist Hans Christian Oersted, learned that a current flowing through a wire would move a compass needle placed beside it. This showed that an electric current produced a magnetic field.

Andre Marie Ampere, a French mathematician who devoted himself to the study of electricity and magnetism, was the first to explain the electro-dynamic theory. He showed that two parallel wires, carrying current, attracted each other if the currents flowed in the same direction and opposed each other if the currents flowed in opposite directions. He formulated in mathematical terms, the laws that govern the interaction of currents with magnetic fields in a circuit and as a result of this the unit of electric current, the amp, was derived from his name. An electric charge in motion is called electric current. The strength of a current is the amount of charge passing a given point per second, or I = Q/t, where Q coulombs of charge passing in t seconds. The unit for measuring current is the ampere or amp, where 1 amp = 1 coulomb/sec. Because it is the source of magnetism as well, current is the link between electricity and magnetism. [source]

1855, Faraday

Faraday was greatly interested in the invention of the electromagnet, but his brilliant mind took earlier experiments still further. If electricity could produce magnetism, why couldn't magnetism produce electricity? In 1831, Faraday found the solution. Electricity could be produced through magnetism by motion. He discovered that when a magnet was moved inside a coil of copper wire, a tiny electric current flows through the wire. H.C. Oersted, in 1820, demonstrated that electric currents produce a magnetic field. Faraday noted this and in 1821, he experimented on the theory that, if electric currents in a wire can produce magnetic fields, then magnetic fields should produce electricity. By 1831, he was able to prove this and through his experiment, was able to explain, that these magnetic fields were lines of force. These lines of force would cause a current to flow in a coil of wire when the coil is rotated between the poles of a magnet. This action then shows that the coils of wire being cut by lines of magnetic force, in some strange way, produce electricity. These experiments, convincingly demonstrated the discovery of electromagnetic induction in the production of electric current, by a change in magnetic intensity. [source]

Maxwell's Equations

Gauss's Law for Electricity: The net outflow of the electric field through a closed surface is proportional to the enclosed charge.
Gauss's Law for Magnetism: The net outflow of the magnetic field through a closed surface is zero.
Faraday's Law of Induction: A time-varying magnetic field induces an electric field (current, if a conductor is present)
Ampere's Law: Magnetic field can be created by an electric current or a time-varying electric field.

Wait, what is this facny inverted triangle?

The inverted triangle symbol is called the nabla (or del) operator. It is a way mathematicians use to describe the shape/properties of a field.

The dot product, indicated with a dot in the first two equations, represents the divergence of the field. The divergence measures the tendency of a field to diverge from a focus point, similarly to rays diverging from the sun.

The cross product, indicated with a small x in the last two equations, represents a curl of the field. The curl measures the tendency of a field to curl, wind around an object, axis, or another field.

Experimental Procedure

Part A. Magnetic field generated by an electric current.

Recently, you studied the behavior of a charged particle in the electromagnetic field. The electric field can accelerate the particle because it carries an electric charge, so the interaction is expected. Moreover, we learned that the magnetic field can change the particle trajectory so it starts moving in circles. Well, that is surprising if we think about electricity and magnetism as separate phenomena.

To explain the interaction between a charged particle and the magnetic field, we assume that a charged particle in motion creates its own magnetic field.

Is that true? How can that assumption be tested?

Connect two batteries in series.
Connect a copper solenoid to those two batteries (Figures 1 and 2).
Measure both voltage and current in the circuit.
Place a small compass on the table, close to the axis of symmetry of the solenoid. Move the compass closer to the solenoid. Is there a magnetic field near the solenoid? How far from the solenoid is the magnetic field detected with your compass?
Is there a magnetic field around the solenoid?
Add the third battery. How far from the solenoid is the magnetic field detected with your compass? Is the magnetic field stronger now?
Add the fourth battery. Repeat.
Write down your observations.

Figure 1.

Figure 2.

Part B. Electric current generated by a time-varying magnetic field.

That hypothesis was suggested by Faraday based on a simple symmetry observed in natural phenomena: if the electric current produces a magnetic field, then the magnetic field should generate an electric current.

Now, we will test that hypothesis.

Connect a copper solenoid to a multimeter (Figures 3 and 4).
Place a magnet next to the solenoid. Does the multimeter show any voltage or current?
Place the magnet in the solenoid. What does the multimeter show?
Move the magnet around and observe the multimeter. What does it show?
Record the highest voltage and the highest current you were able to generate. What does the generated current/voltage depend on? Are those factors the same for voltage and current?
Place the magnet on the axis of symmetry of the solenoid. Move the magnet toward the solenoid and then away from it. Is the reading on the multimeter the same?
Place the magnet on the axis of symmetry of the solenoid. Move the magnet toward or away from the solenoid slowly and then very fast. How do the readings on the multimeter differ?
Write down your observations.

Figure 3.

Figure 4.

Part C. Induction with an electromagnet.

Connect a small copper solenoid to a battery (Figure 5). This is the primary coil.
Connect a large copper solenoid to a multimeter (Figure 6). This is the secondary coil.
Set the multimeter to measure voltage.
Slip the primary coil into the secondary one. Wait a short while. Open and close the primary circuit. Observe the multimeter.
Set the multimeter to measure voltage.
Repeat pt. 4
Place the iron core in the primary coil. Does it change the reading on the multimeter?
Write down your observations.

Figure 5.

Figure 6.

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