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Modes of Vibration: This transparency shows how a given vibrating string may oscillate in several different ways. The base frame, the production of the fundamental as the string vibrates as a whole. L is the length of the string - it is constant for all these modes of vibration. Drop in Left overlay. The string may also vibrate in parts. This results in an oscillation of twice the frequency of the fundamental. This is called the first overtone. Remove left overlay; drop in the right overlay. The string is now vibrating in three parts to produce an oscillation of three times the frequency of the fundamental. This is called the second overtone. In the case of a string instrument in music, the note actually heard is generally a combinatin of the fundamental and several overtones, depending on the characteristics of the particular musical instrument.
Projectile Motion: The base frame shows a characteristic trajectory. The left overlay indicates by red arrows the instantaneous velocity both horizontally and vertically at selected points on the trajectory. It will be noted that the vertical component of velocity, which is sizable at the origin, becomes smaller and disappears at the top of the trajectory and then reverses and becomes larger as the object moves downward. Meanwhile the horizontal component remains constant throughout. Leave left overlay in position; drop in right overlay. The resultant of the velocities in the horizontal and vertical directions are shown by the blue arrows to be tangent to the trajectory and of magnitude which decreases to the top of the trajectory and increases as the object descends.
Electric Field Pattern: The base frame shows two uncharged bodies. Drop in left overlay. This overlay shows the electric field between two similar-charged positive spheres. Note the lines of force radiating out in opposite directions act as though they repel one another. The diagram for two similarly-charged negative bodies would be the same as for these positively-charged ones. Remove the left overlay; drop in right overlay which now shows the electric field between two unlike charges. Note how the lines of force radiating from the two unlike charged bodies seem to attract one another.
Mass Spectrograph: The base frame shows the "velocity selector" portion of the mass spectrograph. Positive ions from a source not shown enter at the top of the chamber in which there are crossed magnetic and electric fields. These ions have various masses and velocities. Only those of a preselected velocity emerge from the chamber at the bottom. Drop in left bottom overlay. The ions now enter a uniform magnetic field at right angles to the direction of motion. Drop in left middle moverlay. A positively-charged ion of mass [M1] moving through this field will travel in a semicircle and fall upon a photographic plate. Drop in left top overlay. The path of an ion of similar velocity but of less mass [M2] will be curved more sharply and travel in a semicircle of smaller radius. Thus the mass spectrograph can separate and thus detect isotopes of different masses of the same element.
Cyclotron: The base frame shows the two hollow "Dess" to which a high frequency alternating current is applied. This results in a constantly changing electric field horizontally between the "Dees." Drop in left bottom overlay. This shows the application of the magnetic field perpendicular to the electric field. Leave in left bottom overlay and drop in left top overlay. The red spiral indicates the path of a stream of charged particles under the influence of the reversing electric field and the steady magnetic field. The particles are accelerated and emerge from the opening in the "Dee" illustrated in the base frame.
Ammeter and Voltmeter: The transparency shows how a galvanometer may be modified to measure current and voltage. The base frame depicts a galvanometer which in itself measures small currents. Drop in left overlay. By placing a low resistance of known value in parallel with the galvanometer, a known fraction of the current bypasses the galvanometer. If the galvanometer is then recalibrated to indicate the total current through both the low resistance shunt and the galvanometer, the combination is now an ameter. Remove left overlay; drop in right overlay. By placing a high resistance in series with the galvanometer, the current that flows through the combined resistance of the galvanometer and the additional resistance is proportional to the voltage applied. By recalibration the galvanometer to read voltage, we now have a voltmeter. An ammeter is a galvanometer with a low resistance in parallel. A voltmeter is a galvanometer with high resistance in series.
Electric Field Between Parallel Plates: The base frame shows the uniform electric field between two oppositely-charged plates. Drop in left, bottom overlay. A conductor placed in the field will experience a separation of the charges as shown. (Free electrons will move toward the side of the conductor nearest the positive plate leaving the other side of the conductor charged positively.) Note that the induced electric field within the conductor is equal to the original field, but opposite in direction. As a result, the total field inside the conductor is zero. Drop in top, left overlay. The field in the space between the plates goes from the positive plate to the conductor and from the other side of the conductor to the negative plate. Remove the two, left overlays; drop in right, bottom overlay. A non-conductor placed between the charged parallel plates will experience a displacement charge as shown. In a non-conductor, the magnitude of the induced field is less than the original field and its direction is opposite to the original field. Drop in right, top overlay. The resultant field outside and inside the non-conductor is shown.
Magnetic Field Due to a Solenoid: This transparaency illustrates the magnetic field around the wires of a solenoid and shows how the field of each individual turn contributes to the production of the total field characteristic of the solenoid. The direction of current in the coil is indicated by the cross at the left end and the blue arrows. Have the students apply the hand rule for determining the direction of the field around a single conductor. This will establish the direction of the field around each loop (counterclockwise at the top, clockwise at the bottom). Then apply the hand rule for the determination of the field around a solenoid. From the transparency, the relationship between the two is readily seen.
LC Circuit: The base frame illustrates the transfer of energy from a capacitor (C) to an inductor (L) and back again in the typical oscillating LC circuit. The base frame shows a capacitor and inductor connected in series. Drop in left overlay. This shows a charged capacitor ready to discharge through the inductor. Remove left overlay; drop in bottom overlay. The capacitor has discharged through the inductor, which now has built up a magnetic field around it which is about to collapse. Remove bottom overlay; drop in right overlay. This illustrates the result of the complete collapse of the field around the inductor, which in collapsing produces and e.m.f. charging the capacitor in the opposite direction. The process is then repeated, thus giving rise to an alternating current in the circuit whose frequency can be caculated.
Induction Coil: The base frame shows the magnetic field surrounding a current-carrying coil which is the primary of an induction coil. As the current starts up in the primary coil, the magnetic field expands outward from the coil. Drop in left overlay. A secondary coil wound around the primary will be in this expanding magnetic field. A current is then induced in the secondary as the lines of force cut past its turns. The direction of the current in the secondary is indicated by the red arrows. Remove left overlay; drop in right overlay. The secondary is now wound in the opposite direction compared with the previous case. With the still expanding magnetic field in the primary, the direction of the induced current in the secondary is shown by blue arrows.
AC Voltage-Current Relations: This transparency illustrates the voltage and current relations in a series circuit containing resistance (R), inductance (L), and capacitance (C). The base frame shows this circuit connected to an A.C. source through an ammeter. It also shows a graph of the current (i) through the circuit as a function of time. Drop in left overlay. This overlay, as shown by the orange line, illustrates the fact that through the resistor the current and the voltage are in phase. Drop in bottom overlay. This overlay shows that the voltage across the inductor is 90^o out of phase with the current through the inductor; the voltage is leading the current by 90^o. Drop in right overlay. The voltage across the capacitor, represected by the purple graph, will be seen to be 90^o out of phase with the current in the circuit. We then say that the voltage lags the current by 90^o. Note the voltage across the inductor is 180^o out of phase with the voltage across the capacitor.
Forces on Charged Particles: The base frame shows a uniform magnetic field B in which two oppositely-charged plates produce an electric field E at right angles to the magnetic field. The direction of the magnetic field is into the plane of the projection as indicated by the Xs. Drop in left bottom overlay. A negatively-charged particle, such as an electron, with a velocity to the right will not be deflected, if the force due to the electric field (upward) is equal but opposite to the force due to the magnetic field (downward). Drop in left top overlay. As the negatively-charged particle moves out from between the charged plates, it is no longer subjected to the electric field. The force due to the motion across the magnetic field is now unbalanced, and the particle, experiencing a certripetal force, moves in a circle as indicated.
Moving Rod in a Magnetic Feild: The base frame shows a metal rod resting on two rails in a space containing a uniform magnetic field B directed into the plane of projection as indeicated by the Xs. a. Induced Current Due to Moving Rod (Generator) Drop in left overlay. If the circuit is completed with an ammeter across the rails, and the rod moved with velocity V to the right, the motion of the rod across the magnetic field causes a current i to be induced in the circuit in the direction shown by the blue arrows. Have the students check the direction of the induced current by the three finger rule for generators. b. Induced Force Due To Current Through Rod (Motor) Remove the left overlay; drop in right. A current supplied by a battery across the rails will produce a magnetic field around the rod which, interacting with the uniform magnetic field B will produce force F on the rod as shown. Have the students check the direction of movement of the rod by the three finger rule for motors.
Cathode Ray Tube: The transparency shows how a stream of electrons is deflected in a cathode ray tube. The base frame shows the construction of the tube,. A heated cathode C is the source of electrons which are accelerated by the high voltahe source toward the anode A. 1) Drop in left overlay. The electron beam emerges through a hole in the anode, passes between the uncharged vertical and horizontal deflection plates, and strikes the screen at the broad end of the tube, causing a spot of light to appear on the flurescent coating on the screen. 2) Remove left overlay; drop in bottom overlay. The upper, vertical deflection plate is now charged negatively; the lower is now charged positively. In passing between these two plates, the negatively-charged electrons are deflected toward the lower plate and the fluorescent spot moves downward on the screen as indicated by the blue dot. 3) Remove bottom overlay; drop in the right overlay. In this case, the horizontal deflection plate in the foreground is charged negatively while the other is charged positively, thus deflecting the beam horizontally across the face of the tube as shown by the green dot. By applying suitable voltages to the horizontal and vertical deflection plates, the "flying spot" can be positioned anywhere on the tube face.
Measurement of the Speed of Light (Fizeau: The base frame shows the system devised by Fizeau for determining the velocity of light. Tt consists of a lens, a glass plate, a rotating toothed wheel, several lenses and a mirror. Drop in left overlay. Light from cource S is made convergent by a lens and, after passing through the clear plate, converges on a notch in a toothed wheel. It is then made parallel by a lens and converged on a mirror by a second lens. The reflected light returns through the notch in the toothed wheel, and is reflected from the surface of the clear plate through a lens, into the eye. If the toothed wheel is rotated, the burst of light passing through the toothed wheel will, upon return from the far mirror, fall on a tooth of the wheel, thus intercepting the light. If, however, the wheel is rotated at the proper speed, the light will pass through one notch and return through the next notch. by extablishing the revolutions-per-minute of the toothed wheel, and the total distance traversed by the light from wheel to mirror and back again, the velocity of light can be established.
Measurement of the Speed of Light (Michelson: The base frame shows a light source, and eight-sided mirror pivoted so that it can rotate, a distant mirror, and an observer. Drop in left overlay. With the mirror stationary, light from the source strikes face A of the mirror, is reflected from this face to the distant mirror, then back to face C, and then to the eye of the observer. If the mirror is now rotated, the light, after being reflected from face A, travels a total distance of about 55 miles back to the octagonal mirror. While the light is traveling this distance, the octagonal mirror has moved so that the returning ray no longer strikes face C. If the mirror is rotated fast enough, the light leaving face A, and reflected from the distant mirror, may return to meet face B which, while the light has traversed the approximate 44 miles, now has come into the position formerly occupied by face C. The light then enters the eye of the observer. If the speed of the rotating mirror to make 1/8 of a rotation. Thus, the speed of light can be measured.
Michelson Interferometer: The base frame shows the important parts of the Michelson interferometer the light source, lens, half-silvered mirror, glass plate and two mirrors. The red lines indicate the paths of rays originating in the light source. One pair of rays travels through the half-silvered mirror to mirror #1, back to the front surface of the half-silvered mirror from which it is reflected to observer. Drop in left overlay. The other pair of rays reflects from the front surface of the half-silvered mirror, moves through the glass plate to mirror #2, then is reflected through the glass plate again, through the h-s mirror once more, to the observer. The two pairs of rays produce and interference pattern in the eye of the observer. Every effort is made to make the path of the two pairs of rays of exactly equal length. It is for this reason that the compensating plass plate is introduced. Drop in right overlay. Any small change in path, such as lightly shortening or lengthening the path of the rays to mirror #1, will cause a noticeable shift in the interference pattern.
Atomic Planes in a Crystal Model: The base frame shows a cubical, crystal lattice similar to that of a sodium chloride crystal. Drop in left overlay. The colored planes are parallel to each other and are parallel to two side faces of the crystal. Remove left overlay; drop in right overlay. Once again, the planes are parallel to each other, but this time they are not parallel to any of the crystal faces. The two sets of planes illustrate two principle axes of a cubical crystal.
Urantum Series: This trasparency traces the radioactive dacay of U238 through successive emissions to the final from of Pb206. The base frame shows a grid on which will be plotted the number of neutrons in the nucleus (N) against the atomic numver (Z). 1) Drop in bottom overlay. U238(Z=92,N=146,Z+N=238) emits a He particle and results in Th234, [92]U238 [2]He4+[90]Th234. 2) Leave in second overlay; drop in next, left overlay. Th234 emits an electron to form Pa234, [90]Th234 [-1]e0+[91]Pa234. In like manner, [91]Pa234 [-1]e0+[92]U234. 3) Drop in third overlay. By a series of a emissions, uranium 234 becomes lead 214. 4) Drop in fouth overlay. After lead 214 decays to bismuth 214, "branching" takes place. Lead 210 is formed by the emission of bismuth 214, followed by an a emission, or by the a emission of bismuth 214 followed by a emission. 5) Drop in the fifth overlay. With the emmission of two betas and one alpha, lead 210 becomes lead 206, which is stable and, therefore, it is the end of this radioactive series. The emission of an a particle decreases the mass # 4, the neutron # 2 and the atomic # 2. The emission of a particle does not affect the mass #, but does decrease the neutron # 1, and increase the atomic # 1.
Damped Harmonic Motion: This transparency shows the plot of the amplitude vs. time for underdamped harmonic motion. Case A shows mechanical oscillations. Case B shows electrical oscillations. The base frame shows no damping in these two cases, Case A shows simple harmonic motion of a mass m on a spring with spring constant k. y=A*cos(wt) w sq root of k/m Case B shows an oscillating LC circuit (no resistance). q=Q*cos(wt) w sq root of 1/LC Drop in the left overlay. This overlay shows the result of exponential damping in these two cases. Case A shows mass m on spring subjected to a damping force proportional to the velocity. FD=bv y=exp(-bt/2m) Case B shows an oscillating LCR circuit (a small damping resistance R). q=Q*exp(-Rt/2L) Drop in the right overlay. This overlay shows the resulting damped harmonic motion in these two cases. Case A shows, y=A*exp(-bt/2m)*cos(w't) w'sq root of k/m-sq(b/2m) Case B shows, q=Q*exp(-Rt/2L)*cos(w't) w'sq root of 1/LC-sq(R/2L)
Superposition of Waves: This transparency shows the first six terms of the Fourier Series for a sawtooth wave. The base frame shows the displacement vs. time axis. Drop in the bottom, left overlay. This shows a plot of y=-sin(wt). Drop in the second, left overlay. This shows a plot of y=-1/2*sin(2wt). Drop in the third, left overlay. This shows a plot of y=-1/3*sin(3wt). Drop in the bottom, right overlay. This shows a plot of y=-1/4*sin(4wt). Drop in the second, right overlay. This shows a plot of y=-1/5*sin(5wt). Drop in the third, right overlay. This shows a plot of y=-1/6*sin(6wt). Drop in the bottom overlay. This plot shows that the sum of plots 1 through 6 (solid lines) approximates a sawtooth wave (dotted line).
Carnot Cycle: The base frame shows the P-V axis. 1) Drop in the bottom, left overlay. This overlay shows the isothermal expansion part of the cycle. The shaded area represents the work done by the gas in the expansion at constant temperature. 2) Drop in the second, left overlay. This overlay shows the addiabatic expansion part of the cycle. The shaded area represents the work done by the gas during the expansion with no heat entering or leaving the system. 3) Drop in the third, left overlay. This overlay shows the isothermal compression part of the cycle. The shaded area represents the work done on the gas during the compression at constant temperature. 4) Drop in the fourth, left overlay. This overlay shows the adiabatic compression part of the cycle. Again, the shaded area represents the work done; this time it is work done on the gas during the compression with no heat entering or leaving the system. 5) Drop in the right overlay. This overlay shows the net work done during the complete cycle.
Electromagnetic Waves:
Biot's Law:
Magnetic Field Due to a Circular Coil:
Plane Electromagnetic Waves: The base frame shows the xyz axis with wave propagation in the positive x-direction. Drop in the bottom, left overlay. This overlay shows the variation in the electric intensith in the y-direction. Drop in the second, left overlay. This overlay shows the variation in the magnetic intensity in the z-direction. Note that the direction of the Poynting vector (S+E*H or s=E*B) is the direction of propagation of the waves.
Moving Charge in a Magnetic Field: This transparency shows the relation between the vectors v, B and F in the expression F=q*v*B. The base frame shows the xyz axis with a positive charge at the origin. Drop in the bottom, left overlay. This overlay shows the field B and velocity v in the x-y plane. Drop in the second, left overlay. This overlay shows the force F at right angles to the x-y plane formed by v and B. The magnetic force vanishes as becomes 0^o or 180^o (v and B parallel or antiparallel). The force has its maximum value when 90^o (v is at right angles to B).
Sphere in an Electric Field: The base frame shows a sphere. Drop in the left overlay. This overlay shows the electric field lines due to a conducting sphere in a uniform electric field. Remove the left overlay, drop in the right overlay. This overlay shows the electric field lines due to a dielectric sphere in a uniform electric field.
Hysteresis: The base frame shows a Rowland ring with the primary (magnetizing) winding. The current is proportional to the magnetic intensity B. Drop in the left overlay. This overlay shows a secondary winding on the Rowland ring connected across a ballistic galvanometer. The galvanometer reading is proportional to the magnetic density B. Drop in the right overlay. This overlay shows plots of B vs. H. The magnetization curve (shown in red) is obtained by steadily increasing the magnetic intensity H from zero, starting with an initially unmagnetized sample inside the Rowland ring. The hysteresis curve (shown in blue) is obtained by increasing the magnetic intensity H from zero to a certain maximum in one direction, then decreasing H to zero, then increasing it to the same maximum in the opposite direction and finally decreasing it to zero again.
E and D Across a Boundary: The base frame shows the vectors E1 and D1 in a dielectric of permittivity 1. Drop in the left overlay. This overlay shows the vectors E1 and D1 resolved into components tangential and normal to the boundary between the two dielectrics. Drop in the right overlay. This overlay shows the vectors E2 and D2 in the second dielectric of permititivity 2. The tangential component of E and the normal component of D are continuous across the normal component of D are continuous across the boundary E1*sin(r1)=E2*(r2) and D1*cos(r1)=D2*cos(r2).
Interference and Diffraction: The base frame shows the plots of arbitrary intensity vs. sin() for 2-slit and 4-slit interference. Drop in the bottom, left overlay. This overlay plots arbitrary intensity vs. sin() for single slit diffraction for the 2- and 4-slit cases, assuming the distance between slits to be four times the slit width. Drop in the second, left overlay. This overlay shows the resultant intessity plot (product of the above interference and diffraction curves).
Young's Experiment: The base frame shows thelight source, a single slit, double slits and a screen. If the light source is a laser beam, the single slit is unnecessary. Drop in the left overlay. This overlay shows the Huygens cylindrical wavelets diverging from the single and double slits. Drop in the right overlay. This overlay shows the rays from both slits interfering at a point P on the screen.
Reference Frames: The base frame shows the fixed coordinates xyz. The overlay shows the sliding coordinates x'y'z'.
Field due to an Oscillating Dipole: