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Class_Notes

February 2, 1999.... Physics 201B... Spring 1999

Comments:

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. Newton's Law for the mass-spring system is:

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. Equating the voltages across the two devices:

Note the comparison... spring is like capacitor, mass is like coil... x is like q.... v is like I.

Tesla Coil (Combination of Transformer and LC oscillators)

Film

Segment A is a transformer, increasing the voltage to about 15,000 volts (with corresponding decrease in current). Coil and capacitor form oscillating circuits (B) which change frequency from 60 cycle/sec to 1,000,000 cycles/sec. Final transformer (C) increase voltage to over 1,000,000 volts. When voltage is applied to endpoints of coil, it creates electric fields which are oscillating at 1,000,000 cycles/sec and strengths which cause air to ionize and create sparks.

Electromagnetic Waves

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.

Waves

I believe we all know what a wave looks like

This picture of a wave shows the amplitude of the wave above and below the normal position of whatever is "waving".

The wave is composed of peaks called CRESTS and low points called TROUGHS. There is a repetition of crests and troughs.

The horizontal line can represent EITHER time OR distance...

If it represents time, then the time between adjacent crests is called the PERIOD (T). In the figure, the period is 1 second per cycle. The reciprocal of the period (1/T) is called the FREQUENCY (f) so in this case it would be 1 cycle per second. If period were 0.1 second per cycle, then frequency would be 10 cycles/second.

If it represents distance, then the time between adjacent crests is called the WAVELENGTH (l). In the figure, the wavelength is 1 meter/cycle.

The velocity (v) of the wave... the speed you would move if you "sat" on a crest and moved with the wave is calculated by

But to understand waves we need to start with a single harmonic oscillator which has a period and frequency but no wavelength.

We can compare simple harmonic motion with circular motion in Interactive Physics.