Electric currents (i.e. moving electric charges) can create magnetic fields.

In fact, magnetic fields created by ferromagnetic objects are also created by “nanocurrents”: spinning electrons.

All materials contain atoms, and all atoms contain negatively charged electrons. Each electrons is always spinning like a top, so constitutes a tiny circulating current, just like a coil of wire.

In most materials, the electrons pair up, with the two members of the pair rotating in opposite directions, so their magnetic effects cancel.

However, in ferromagnetic materials, these electron “spins” do not pair up. Instead, most of the electrons are spinning in the same direction, resulting in net magnetism, either hard ferromagnets, if domains align, or soft ferromagnets, if they do not. (One domain will contain billions of spinning electrons.)

So even though there are no measurable currents in a ferromagnetic material, microscopic electron “spin currents” give rise to magnetism.

Oersted: Electric currents create magnetic fields.** Faraday: Magnetic fields that change with time create electric fields -- magnetic induction.

The resulting voltage from this electric field is called an “induced EMF”.

(measures current)

If you move a magnet near a coil of wire (a solenoid) that is part of a complete circuit, the induced EMF will create a current. The current will have opposite directions when the magnet moves in and when it moves out. The current will also change direction if you switch the poles of the magnet.

The induced current will create its own magnetic field. Lenz’s Law: The induced magnetic field will oppose the change that created it.[That is, as the N-pole is entering the solenoid, the induced current is have its own N-pole on the left. As you remove the magnet, the induced current will have its N-pole on the right.]

Consider a coil rotating between poles of a magnet.

In the reference frame of the coil, the magnet, and its magnetic field (B) are rotating. Therefore, the induced current keeps changing direction, at the frequency of the rotation.

If the coil is rotating with a constant angular speed, ω = 2πF, the induced current and voltage will be sinusoidal.

F t = t / T0.0 0.5 1.0 1.5 2.0

V /

V0 =

I / I

0

-1.0

-0.5

0.0

0.5

1.0 This is the basic idea of a generator: it turns mechanical energy (a rotating coil) into electrical energy: the mechanical power put in (to turn the coil inside the magnet) gets turned into electrical power out (I⸱V).

Oscillating currents and voltages are called AC-currents and AC-voltages (“AC” means alternating current), whereas a battery, which gives a voltage that doesn’t change with time, gives a “DC” current & voltage). (“DC” means direct current.)

Hydroelectric Generators

[In coal, gas, or nuclear power plants, the fuel is used to heat water and the turbine is turned by steam.]

Now, suppose there is no external force turning a coil (which is free to rotate) but instead the coil is connected to an AC-voltage. The current in the coil will make a magnetic field perpendicular to the coil. The coil will turn to make its “N-pole” point toward the S-pole of the magnet, but it may overshoot (due to its inertia). One half-period (of the AC current) later, the coil’s magnetic field points in the opposite direction, so instead of the coil “turning back”, it keeps turning in the same direction.

We have now made a device that turns electrical energy (from the AC-source) into mechanical motion: we have made a motor.

So a motor and generator are basically the same device: the generator turns mechanical energy into electrical energy and the motor turns electrical energy into mechanical energy.

Now consider applying an AC current to a coil (with no external magnet). It will create an oscillating (and therefore changing) magnetic field, which will in turn induce an electric field and voltage (the EMF) that (from Lenz’ Law) will try to oppose the changes in the original current and field. [Signs get confusing !!!]The net result is, that if the resistance of the call is tiny (i.e. negligible), the net AC-current and voltage are 90o out-of-phase.

F t = t / T-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

I / I0V / V0

The coil is called an inductor with self-inductance

L = V0 / (2πF I0)[L is measured in Henry’s: 1 H = V⸱s/ A]

Inductors often have a ferromagnetic core inside the coil (to make the magnetic field and induced EMF larger) and typically have values 10 μH to 0.1 H.

The inductor stores energy in its magnetic field. The energy density (i.e. energy/volume) is proportional to B2.

Similarly, the energy density stored in an electric field (e.g. between the plates of a capacitor), is proportional to E2.

TransformersNow consider two coils wrapped around the same soft ferromagnetic “core”. The purpose of the core is not only to increase the magnetic fields produced by currents but to confine the magnetic flux lines so that all the magnetic field that passes through one coil passes through the other (i.e. no magnetic field leaks out). One coil (the primary) is attached to an AC-voltage source; the other coil (the secondary) is attached to a device to which we want to apply electrical power – here shown as a resistor.

The description in the text may be confusing -- here is a simplified discussion:

If no magnetic field leaks out, the same number of flux lines pass through every turn of both coils. Therefore, each turn will have the same induced field and EMF. Therefore, the total voltage of each coil will be proportional to the number of coils:Vsecondary/Vprimary = Nsecondary/Nprimary

If no magnetic field leaks out and no energy is wasted [e.g. no energy is lost when the field in the core changes (e.g. the core doesn’t conduct electricity) and if the wires of the coils have negligible resistance compared to R], then all the power input at the primary will be dissipated in the resistance connected to the secondary:

Pin = PoutIprimary Vprimary = Isecondary VsecondaryIsecondary/Iprimary = Vprimary/VsecondaryIsecondary/Iprimary = Nprimary/Nsecondary

V2 / V1 = N2 / N1P2 = P1

(I2 / I1 = N1 / N2)

If N2 = N1, the primary and secondary voltages (and currents) are equal, but it has the advantage of separating the input, Vin, from the output, VR. It is therefore called an isolation transformer.

If N2 > N1, the output voltage is greater than the input voltage. This is called a step-up transformer.

If N2 < N1, the output voltage is less than the input voltage. This is called a step-down transformer. [Most electronic devices use a step-down transformer to change from 120 V from the wall to a small voltage needed for semiconductor electronics, typically ~ 15 V. Also, a “rectifying” circuit must be used to change the AC voltage to DC, needed for the electronics.]

V2 = VR

A transformer can only work with an AC voltage, since it depends on the magnetic field changing (periodically) with time.

V1 = Vin

Text’s figure of Isolation Transformer

Text’s figure of generator Our previous figure of generator

The text’s generator differs from the one we discussed earlier in that in our case, the generated AC-voltage was taken directly from the rotating coil (the rotor), whereas in the text’s case, it comes from a secondary coil linked to the rotor through a magnetic core – i.e. the output is isolated from the rotor (a good idea).

Text’s figure of isolation transformer Text’s figure of motor Our previous figure of motor

The text’s description of a motor differs from our simple, previous description. In our description, the input AC-voltage is applied to the rotor (and so oscillates the coil’s magnetic field), whereas in the text’s model, the AC-voltage is applied to a primary coil which then oscillates the large field of the ferromagnet; the results will be similar but applying voltage to the stationary primary coil is simpler. In fact, AC-voltages are often applied to both to keep the speed of the rotor locked (“synchronized”) to the AC frequency.

Power Transmission

Suppose you have an electric appliance (light bulb, toaster, dryer, washer, …) that requires a power (energy/second) P to operate. Since P = V ⸱I, this power can be provided by using a high voltage and low current or large current and high voltage, as long as the product is correct.

The problem with using a high voltage is that it is dangerous: if someone touches the outlet or a wrong spot on the appliance, they can be killed.

The problem with using a high current is transmitting the current from the power station: if the current, I, has to flow through wires from the power station to the home, some voltage will be lost due to the resistance of those wires: ΔV(wires) = I ⸱ R(wires).

Transformer: V2 / V1 = N2 / N1P2 = P1

I2 / I1 = N1 / N2

The solution is to transmit the power using high voltage and low current and then using a step-down transformers to increase the current and lower the AC voltage to a safe value.

In the U.S., supplied AC power is nominally at F = 60 Hz and 120 V.[This is the effective “rms” voltage that gives the same amount of power as 120V DC; the peak AC voltages is 120 V ⸱√2 ~ 170 V.]

F t = t / T0.0 0.5 1.0 1.5 2.0

V (v

olts

)

170

85

0

-85

-170

Actually, the frequency and peak voltages can vary. 115 V is more common than 120 V (and can be as low as 110 V) and frequencies may dip a few Hz below 60 Hz at peak-use hours.

“hot” terminalneutral terminal (at 0 V)

“ground” –attached to a rod sunk in the ground to prevent the case of a faulty appliance from developing a voltage

Exercises:20.One type of microphone has a permanent magnet and a coil of wire that move relative to one another in

response to sound waves. Why is the current in the coil related to the motion? 21. If the primary coil of a transformer has 200 turns and is supplied with 120-V AC power, how many turns

must the secondary coil have to provide 12-V AC power?23.The primary coil of a transformer makes 240 turns around the iron core, and the secondary coil of that

transformer makes 80 turns. If the primary voltage is 120-V AC, what is the secondary voltage?25. If an average current of 3 A is passing through the primary coil of the transformer in Exercise 23, what

average current is passing through the secondary coil of that transformer?27.A magnet hanging from a spring bounces in and out of a metal ring. Although it doesn’t touch the ring, the

magnet’s bounce diminishes faster than it would if the ring weren’t there. Explain.28.The high-voltage spark that ignites gasoline in a basic lawn mower engine is produced when a magnetic

pole moves suddenly past a stationary coil of wire. From where does that spark’s energy come?29.Suppose you include an inductor in an electric circuit that includes a battery, a switch, and a lightbulb.

Current leaving the battery’s positive terminal must flow through the switch, the inductor, and thelightbulb before returning to the battery’s negative terminal. The current in this circuit increases slowlywhen you close the switch, and it takes the lightbulb a few seconds to become bright. Why?