January 26, 1999.... Physics 201B... Spring 1999
Will open up first test... on electricity and magnetism.. next week... in Web CT... it will be self-graded...
We will use the same "cooperative"means as long as EVERYONE understands the concepts and ALL can answer the questions on their own after the discussion. Remember that the goal is that all have learned physics...
I would like each one to create their account on the Web...
Recall that a mass, M, creates a field, g, which creates a force on a mass, m, given by F = mg.
Recall that a charge, Q, creates a field, E, which creates a force on a charge, q, given by F = qE.
If we put a mass in a gravitational field and apply Newton's Law to it... we get:
If we put a charge in an electric field and apply Newton's Law to it... we get:
What happens when we move a mass through a gravitational field?... when we move a charge through an electric field?
If we move the mass m from a to b (a distance d) through the gravitational field, we do work (Fpath d) and the mass gets a change in potential energy. DPE = mg d
If we move the charge q from a to b (a distance d) through the electric field, we do work (Fpath d) and the charge gets a change in potential energy. DPE = qE d
We now define the change in potential energy per unit charge as the change in VOLTAGE. DV = DPE / q = E d.
The equivalent concept in gravity would be to divide DPE by m, the change in potential energy per unit mass... DPE / m = g d.. which is not usually discussed in texts...
Notice that DV has the units of Joules/Coulomb... Thus a 9 volt battery means that a coulomb of charge at the positive terminal of the battery contains 9 Joules of potential energy.
Where does the energy, that the charges have, come from???
What forces + charges inside a battery to accumulate on the anode and forces - charges inside a battery to accumulate on the cathode... it is the chemicals which give up their chemical energy to give charges potential energy.
Symbol for battery:
Now we can spread Q in whatever shape we want... for example, if we take two parallel metal plates (called a capacitor) and put positive charge (Q) from the anode on one plate and negative charge (-Q) on the cathode... we create a uniform field between the plates... which now stores the energy of the charges on the capacitor.
Suppose we shot an electron into the region between the plates as shown... which way would it go?
Suppose we shot an electron out of the paper into the regions shown... which way would it go?
An inside look at a TV... a love affair between unlike charges?
We saw in the last class that moving charges create a magnetic field. Now we want to look at moving charges and see other applications. A positive charge flowing in one direction is equivalent to a negative charge flowing in the opposite direction. We DEFINE current as the direction in which positive charge flows.
When current flows in most metals, it is the electrons which carry the charge. The metal does NOT become charged when current flows because when electrons flow, they are replaced by elcctrons coming in the other end of the wire. There are always as many electrons in a section of wire as there are protons. In typical flow electrons move very slowly... (or order of cm/s).
Some simple applications using batteries and capacitors in circuits...
Basic circuit rule: In any closed path.. energy supplied to the charges in the battery must be "lost" to elements that it flows through.
When the switch S is in contact with point A, charges flow from battery onto capacitor and are stored there. When the switch is moved to point B... the charges from the capacitor rush rapidly through the flashbulb and create a sudden flash of light.
Batteries and Bulbs:... assume 9 volt battery...
Two bulbs in "parallel"... each one is in a separate closed loop with the battery so each lighbulb will get the full 9 Joules per coulomb and both will be fully lit as if it were the only bulb in circuit... this is the way the circuits are in the house... things pluged into adjacent plugs are in parallel... As you plug more elements in, you draw more current from the battery until it can't supply any more current.
Bulbs in series... half of the 9 Joules for each coulomb will be "lost" in each bulb since the charges have to go through each bulb so the bulbs will not be as bright as in the circuit above.
AC circuits in home...
Generator supplies alternating current... AC battery
Attach to a coil...to create alternating magnetic field in coil...
Recall, in capacitors we store "charge" on plates creating an electric field... storing electric energy.
Now, in a coil, we use "currents" in the coil creating a magnetic field... storing magnetic energy.
Transformers: Use the changing magnetic field in one coil to change the magnetic field in another coil has become a very useful way to link circuits without direct current flowing from one coil to the other. The key to this linkage... if all the magnetic field goes through both coils... that the power is the same in both coils...
Power is defined as DPE / Dt = Dq DV / Dt = I DV
Thus if the voltage difference on the first coil is 120 V and the current is 10 amp... and the voltage difference in the second coil is 1200 V then the current then the current in the second coil would be 1 amp. The method to do this increase in voltage is accomplished by having 10 times as many turns in the second coil as in the first coil. This is the method that is used to transmit power across the country in order to not lose thermal energy with high currents.
Electrical Oscillators (Comparison to Mechanical Oscillators).
Connecting a capacitor and a coil together is equivalent to attaching a mass to a spring....
In the mass-spring system... we have two types of energy... spring potential energy and mass kinetic energy which cycle back and forth at a frequency which depends on the spring constant k and the mass m.
In the capacitor-coil system... we have two types of energy... capacitor electric energy and coil magnetic energy which cycle back and forth at a frequency which depends on the capacitor constant C and the coil constant L.
If we attach an electromagetic oscillator to an antenna through use of a transformer as in the figure below, we create electric and magnetic currents as charges move back and forth in the antenna. These electric and magnetic waves combine to form an electromagnetic wave which moves away from the antenna at the speed of light.
The arrows represent the electric fields created when the positive and negative charges at the ends of the antenna as the charges oscillate back and forth. The X and O represent the magnetic fields into (X) and out of (O) the paper. Note that the waves will travel away from the antenna. If you put the fingers of your right hand along the electric field vector and curl your fingers toward the direction of the magnetic field, the thumb will point in the direction of the wave's velocity.
Actual sources of electromagnetic waves.
gamma rays. 1021 Hz osc. of charges in nucleus
xrays. 1018 Hz osc. of inner electrons of heavy atoms
ultraviolet. 1016 Hz osc. of electrons in atoms
visible. 1015 Hz osc. of outer electrons in atoms
infrared. 1013 Hz osc. of atoms and molecules
microwaves. 1010 Hz osc. of current in short antenna
radiowaves. 107 Hz osc. of current in long antenna
Waves at all these frequencies can be created by radiation of bodies at high temperature. There is a distribution of radiation that was developed to show how much of each frequency would be sent out. (In explaining the "physics" of this distribution, Planck introduced the need to treat electromagnetic waves as photons.) For example, the surface temperature of our sun is about 6000K and the most intense part of its spectrum is at the center of the visible spectrum. A hotter body is called a blue star because the center of its spectrum is toward the ultraviolet end of the spectrum.