### Magnetic Fields

Electromagnetic Induction

In a comon dc circuit, electrons move at speeds of:

a) centimeters per second.

b) the speed of a sound wave.

c) thousands of kilometers per second.

d) the speed of light.

e) none of these.

### Resistance

If you could somehow see microscopically inside the filament of a light bulb carrying electric current, you would see electrons accelerating in the direction of current flow. They would occasionally run into the atoms making up the filament, and would be scattered like a pool ball hitting another, much larger ball.

This scattering of electrons reduces their energy and transfers it to the atoms of the filament. The atoms of the filament can be thought of as vibrating from the collision. Some of this energy of vibration would go towards making light. Most would be lost as heat energy transfer to the surroundings.

Electrons colliding with atoms amounts to resistance to their passage through a material.

As mentioned before, most metals are good conductors of electricity (electrons), so they resist the flow of electrons less than other materials, and are used to manufacture pathways for electron flows-- wires. Other materials, e.g. most plastics, ceramics and rubber products are highly resistant to electrons passing through them-- we call them insulators. These materials are used to clad wires, preventing the electrons from leaking out of the wire or jumping to another wire.

Some poor resistors (good conductors):

• metals

Some good resistors (poor conductors):

• ceramics
• rubber

One analogue for voltage, current flow and resistance is show below:

The green part of this analogous model shows a way to visualize what happens as electrons pass through conducting materials. Marbles on the top have more gravitational potential energy than do those at the bottom. Hence, they roll down the slanted surface. This is analgous with the case of electrons in a wire connected to a battery in a circuit, where the battery's voltage (charge push) works to accelerate them..

As the marbles roll down, they collide with some of the posts, and lose energy to the posts. The posts vibrate from the collisions. This is analgous to electrons colliding with atoms in a material, losing energy to the atoms, and heating the atoms as a result. The filament of an incandescent heats up following this analogy, and the result is light emission as the atoms cease to vibrate (before the next electron-atom collision).

A material that has more resistance to the flow of electrons can be thought of as having more posts per area of material. Wires, which have low resistance to electricity (and are called good conductors) have fewer "posts."

The above analogy falls short in that you might imagine that the marbles would travel faster in the feeder trays (wires) than in the resistive material (light bulb element).

In the case of electricity, the current is the same everywhere in the wire, the connected bulb filament, and the wire leading away from the bulb, which means that the same number of electrons are crossing per second at each location along the path. In real circuits, the resistive circuit elements cause 'traffic jams' which propagate backwards (and forwards) along the current path. The propagation is easily explained, electrons can push one another at a distance, without touching. Thus changing the motion of an electron moving (slowly!) through the filament affects those in front and behind it.

Also, don't think that the electrons coming out of one end of a wire are the same ones going in the other end, as is true for our "marble-electrons."

### Power

When speaking of macroscopic objects in motion, we defined Power as work done per unit time (units of energy in J (joules) per time (seconds). A joule per second is a watt (W).

Recall that voltage is energy/charge (units joules/coulomb) and that current is charge moving over time (units are coulombs/second). Thus voltage times current, V x I, is energy per time, or power:

Some of the power supplied to any circuit is lost as "heat," the increase in average kinetic energy of atoms and molecules of metals, air, water, pins hit by marbles, etc. In electrical circuits this process is known as "Joule heating," named after James Prescott Joule. Using Ohm's law to substitute for voltage, one can see that power is given by:

Fuses exploit this principle. If a "short" occurs in a circuit, a path for electricity to flow that has too little resistance, then current will increase through the entire circuit. As long as the fuse has the least tolerance for heat, the increased current will heat the element of the fuse until, eventually, it will melt, breaking the circuit.

### Power Transmission

Large currents in wires produce "Ohmic heating" of the wire, with the power lost to heating described by:
Pheat = I2R.
To circumvent this problem, electric energy is transmitted along high voltage lines, where power is maximized by increasing voltage, not current:
Power = Voltage x Current: P = V I
Long distance electric lines may operate at 120,000 volts!

### Magnetism

 Why can magnets pick up nails and paper clips? During the last lecture we considered how a charged balloon sticks to a wall. This phenomenon was called "polarization." Note that the wall doesn't have to be charged for the charged balloon to stick to it. Also note that the force owing to polarization between a charged and uncharged object is always attractive. Finally, note that the magnetic force between nails, paper clips, etc., and magnets is also always attractive.

So what happens when a magnet is brought near a paper clip?

It turns out that magnetism can be explained by circulating or spinning charges. In particular, the electrons moving about the nucleii of atoms give rise to magnetism.

Electrons have charge, and when they are in motion within atoms-- either in "orbits" moving around nucleii, or because of electron "spin" (akin to them spinning on an axis), they create magnetic fields. (Magnetic "fields" are a convenient way to describe magnetism.)

The most common kind of magnetism, called ferromagnetism, occurs when the magnetic fields in atoms of certain kinds of metals (e.g., iron, nickel) align strongly. Think of a bunch of tiny bar magnets balanced on sticks so they can spin easily. The magnetic field of one of the tiny magnets affects others nearby, causing them to spin and align with it. This normally occurs in clusters of adjacent atoms called domains. Even unmagnetized chunks of iron have domains.

Examination of the domains of a chunk of unmagnetized iron would show that the fields of the domains are randomly aligned with respect to one another. If we denote each domains field with an arrow, here is what this might look like:

We now know that, in ferromagnetic materials, a external magnetic field (surrounding, say, a permanent magnet) will affect the domains of the nails and paper clips. The effect of domain alignment causes the nail or paper clip to become temporarily magnetized, and it will be attracted to the permanent magnet.

What are those funny lines scientists are always drawing around magnets? What are they about?

Magnetic field lines are a way to show the direction and strength of magnetic forces. The direction of the field line shows the direction of push or pull that a magnetized particle would have. The density of field lines indicates the strength of the field.

Christian Orsted observed in 1819 that a wire carrying a current (charge in motion) produces a magnetic field. This is how electromagnets work- current flows through a coil of wire, the optimal arrangement of wire for producing a strong magnetic field. One can observe current producing a magnetic field by placing a compass next to a wire carrying current:

One can reinforce the current-carrying wires magnetic field by winding it into a coil. This gives a stronger magnetic field. The field lines from this coil resemble those of a bar magnet.

This is perhaps better demonstrated with the fabulous jumping wire demonstration.

### Electromagnetic Induction

If moving (e.g., spinning or orbiting) charge results in magnetism, can a magnet be manipulated to move charge?

It appears that a changing magnetic field can cause charge to move. More specifically, the changing magnetic field creates a voltage (charge push) which can cause current to flow. We can have that electric current flow through a circuit and do useful work for us.

Let's spend a few minutes discussing the particulars of how this happens, and comparing motors to generators.