Electromagnetism

Electron Beam Deflection

A large transparent Crookes tube filled with low-pressure hydrogen gas makes a clearly visible "beam of electrons." The beam is deflected with a magnet placed near the tube or by applying voltage to the deflection plates inside the tube. The power supply has a 6.3V AC output for the cathode and a variable DC output for the anode.



Note: The room should be darkened to make the beam visible.

Magnetic Field Around Wire

The apparatus is shown in the picture on the right. It consists of a round plexiglass table with a perpendicular aluminum rod through its center. Two contacts for the banana cables are attached at either end. The maximum current through the rod should not exceed 10 A. The rotation of compasses shows the magnetic force. This demonstration requires a video camera suspended above the apparatus (see picture to the left).

List of parts:
  1. Apparatus
  2. Banana cables
  3. Power supply with current eliminator
  4. Compasses (2 or 4)
  5. Video camera on tripod
Notes:
  • Aligning 2 compasses with the longitude allows them to turn 90° in opposite directions when the current goes through the rod.
  • If 4 compasses are used, one of them will not turn.

Magnetic Field of Parallel Currents

Two light insulated aluminum ribbons are suspended parallel to each other on a metal frame. The length of the ribbons is approximately 1.5 m. A huge home-made double knife switch (pic. 1) is used to redirect currents through the ribbons. Current through ribbons is 120 A, so the circuit should not be closed for more then 5 seconds. Current is limited by a 1.5 kW, 0.08 Ω resistor and a 12 V deep-cycle marine battery serves as the power source (pic. 2).


Pic.4

Pic.1

Pic.2

Pic.3

Picture 3 shows the schematic of the setup: battery (B), resistor (R), switch (S), and parallel ribbons (W).

The repulsion and attraction of the currents is clearly visible even in large classrooms. The entire setup fits on a lab cart (pic. 4).

Ampere Force

An aluminum rod is suspended between the poles of a large magnet. If there is no current through the rod, it swings freely. When the rod carries a current, there is a force which pushes or pulls the rod, depending on the direction of the current.

Note: Use a double knife switch to change the current's direction.

Faraday's Law — Electromagnetic Induction

Two versions of how to demonstrate electromagnetic induction are available.

The "modern" version, shown on the left, requires a special oscilloscope with memory capabilities and several attempts to capture the pulse of the induced voltage in the middle of the display. A magnet is dropped through a coil which is attached to an oscilloscope. A video camera should be used to display the pulse on a big screen in the auditorium.

The "classic" version, shown on the right, can be performed by quickly inserting and removing a magnet into the coil. The OHP ammeter shows the value and direction of the induced current.

Induction Coils

Several important demonstrations can be performed using the same induction coil with or without an iron rod.
  1. Magnetic properties of a current-carrying coil
  2. Energy stored in a magnetic field
  3. Mutual inductance
Energy stored in a magnetic field

List of parts:
  1. DC power supply - 40V 1.5 A
  2. Large induction coil - 3400 turns
  3. Short iron core - 75mm diameter
  4. Light bulb - 120V 15W
  5. Momentary switch
Procedure:
  1. Assemble the circuit as shown.
  2. Without placing the iron core inside the coil, press the switch. The light bulb will shine dimly and turn off with no visible effect once the switch is released.
  3. Place the core inside the coil and press the switch again. Releasing the switch will produce a burst of light from the bulb and a spark between the contacts of the switch. It is best to perform this demo with the lights dimmed.

RL Circuit

This demonstration shows how an RL circuit responds to positive and negative square pulses. The input signal and the voltage across the inductor are displayed simultaneously on the oscilloscope.

List of parts:
  1. RC/RL demo circuit
  2. Oscilloscope
  3. Function generator
  4. Video camera (for a large class)
Notes:

Low-Pass and Hi-Pass Filters


Pic 2

Pic 1

This demo is designed for students who have already learned the basics of RC and RL circuits. Through this demo, students can see one of the applications: simple low-pass and hi-pass filters. Students will be able to understand how the rearrangements of R and L or R and C components can produce opposite effects. Pic 3 and 5 shows two boards, one with a coil and a resistor, and the other with a capacitor and a resistor. Each board is connected to a function generator, an oscilloscope, and an audio amplifier with a speaker (Pic 1 and 2). Wiring diagrams are shown in Pic 4 and 6.

Pic 3
Pic 4
Pic 5
Pic 6

Lenz's Law — Lamp in series with inductance

After closing the switch, bulb 2, which is in series with the coils, reaches full brightness about one second after bulb 1, which is in a parallel circuit. If the iron core is removed from the coils, no delay can be observed.


List of parts:
  1. Power supply (40V @ 500mA)
  2. Three large coils
  3. Large iron core (37cm high x 7.5cm diameter)
  4. Two miniature light bulbs (14V) mounted on plexiglass board
  5. Rheostat (to compensate for the resistance of the coils)
  6. Knife switch

Lenz's Law - Wonder Tubes

Two similar looking cylinders, one magnetic and the other non-magnetic, are dropped down a 1.5 m long aluminum tube. The magnetic cylinder will fall much slower than the non-magnetic cylinder. The figure on the left shows the induced currents and configuration of the magnetic field as the magnetic cylinder falls.

Lenz's Law - Jumping Ring


Pic. 1

Pic. 2

Pic. 3

A coil with an iron core and two aluminum rings is used to demonstrate electromagnetic induction and Lenz's Law. One of the rings has a slit cut in it, and the other does not (see picture 1). The rings are placed around the core. When the apparatus is turned on, the solid ring is ejected into the air. The ring with the slit remains. The effect is enhanced if the ring is cooled with liquid nitrogen.

If the button is held down and the ring is dropped from the top of the iron bar, it will remain suspended as shown in picture 2.

The apparatus also includes a light bulb attached to a small copper coil which shines when the coil is placed around the core and the button is pressed.

Eddy Current Pendulum

Three bobs, made from copper, with the same surface area are available for this demonstration. One has deep narrow slits to diminish the Eddy currents' circulation. It has the same mass as one of the solid bobs, while the third solid bob has half the mass. The solid pendulum's bob stops between the magnet after being released. The bob made with slits oscillates freely.

Transformer

Coils with different number of turns allow the instructor to set up several step-down and step-up circuits. The ratio and phase difference between Vin and Vout can be seen on the oscilloscope.

List of parts:
  1. Transformer with interchangable coils -
    200 turns (1), 400 turns (2), 800 turns (1)
  2. Connecting wires
  3. High power function generator
  4. Oscilloscope
  5. Video camera

Motor-Generator

A simple, large model can be used to generate current or to work as an electric motor. The magnets, brushes, coils, and terminals are clearly shown.

To demonstrate the ability to generate current, connect the terminals to an OHP ammeter and spin the rotor by hand. The generated current is usually very low (approximately 0.5mA). The instructor could show how current depends on the speed of rotation. The picture to the left shows the setup for the generator.

To demonstrate how an electric motor works, the terminals should be connected to a 12V DC power supply. When the motor rotates, it consumes approximately 3A. The picture on the right shows the setup for the electric motor.

Bicycle Generator

A bicycle with gears attached to an electric generator powers 3 headlights that can be turned on successively. It is noticably more difficult to pedal after each light is turned on. A voltmeter and ammeter are attached to the bicycle handlebars and measure the generated power as the student pedals.


Note: A dolly from the stock room is required to move this heavy platform with a bicycle and a generator. The demonstration is located in the Thimann Labs building (in one of the undergraduate labs). Please give at least 3-days' notice when requesting it.

RLC Resonance

The pictures below show simple RLC resonance circuits. The resonance occurs at the frequency of 637 Hz. This resonant frequency can be changed by inserting an iron core into the coil. If the core is fully inserted, the resonant frequency is reduced to 250 Hz. The same parts can be used for parallel and series resonance circuits. For the parallel circuit, a 200 Ω resistor must be used to separate the function generator from the resonating circuit. The resonant frequency remains almost the same for both circuits.


Capacitor and coil with square iron rod inserted
List of parts:
  1. 25 uF capacitor and 400 turn coil with optional square iron rod
  2. Functional generator
  3. Oscilloscope
  4. Two OHP voltmeters (optional)
  5. Wires and cables
Note: For more advanced courses, it is possible to measure the voltages across the capacitor, across the coil, and across the function generator. Using the overhead projector and OHP voltmeters, these values can be compared simultaneously at the resonance frequency.

Jacob's Ladder

This demo shows an electric arc that rises between two vertical conducting bars separated wider at the top. Once the arc reaches the top of the "ladder" and vanishes, another is generated at the bottom to repeat the cycle.

To show how high the temperature of the arc is, the instructor can place a piece of paper between the rods. The rising arc will burn the paper.

Notes:

Tesla Coil

Our newly built Tesla coil can generate 1.2 million Volts of high frequency. It can produce long noisy sparks, and is one of students' most favorite demonstrations. A 12" tall tabletop version of a Tesla coil is also available.

Notes:

Electron Velocity Selector; Finding e/m Ratio


Pic. 2

Pic. 1

A specially designed vacuum tube with a luminescent screen is used for both demonstrations. A glowing trace on the screen represents the path of the electron beam. The vacuum tube has terminals for applying high voltages to the electron gun (3,000 V) and across the deflecting plates (500-600 V). The cathode of the tube is heated by 6.3 V (AC). Vacuum tube is secured on a special stand between 2 Helmholtz Coils that provide a uniform magnetic field across the space between deflecting plates. The whole setup is shown in Pic. 2.



Pic. 4

Pic. 3

Part 1: Electron Velocity Selector

Electron velocity selections are made by applying combinations of electric (E) and magnetic (M) fields perpendicular to the electrons' path as well as to each other. Only electrons with velocity v=E/B trace a straight line on the fluorescent screen. Picture 3 shows how the E field alone affects the electron beam. Picture 4 shows what the beam would look like if it was affected by only the magnetic field.

The instructor can increase or decrease the electrons' velocity by changing the voltage applied to the tube within the range of 1,000 - 3,000 V.



Pic. 5

Part 2: The e/m Ratio

In addition to the electron velocity value obtained in part 1, further measurements are needed to calculate the e/m ratio.

The electric field should be switched off so that only the magnetic field remains. In a uniform magnetic field perpendicular to an electron beam, the trace on a fluorescent screen takes shape of an arc (see pic. 5). The arc formed is a portion of a circle where radius can be used to calculate the e/m ratio with the following equation:  evB = mv2/R.


Pic. 7

Pic. 6

Notes

  • Demonstrations should be provided with lights dimmed.
  • Videocamera is required for large classes.
  • Reference for connecting the coils to a power supply and to each other is shown on pic. 6.


Pic. 8

Appendix

The radius of the arc can be easily calculated by measuring the deflection on the grid and applying basic geometry (see pic. 7). The following formula can be used: R = (AB^2+h^2) / (2h).

Strength of the electric field is E=V/d, where V is the voltage applied to the plates and d is the distance between plates.

A Helmholtz Coils configuration is shown to the left (pic. 8). The equation for a uniform magnetic field between coils is B = (8m0 N I)/(5^(3/2) r) , where μ0 is the permeability of free space, n is the number of turns in each coil, I is the DC current through coils, and r is the radius of a coil.

If the instructor, during the demonstration, comes up with values close to the ones listed in this table, then the calculated e/m ratio will be within 10% of the actual constant.

V = 600 V n = 320
I = 0.55 A d = 5 cm = 5×10-2 m
μ0 = 4π×10-7 N/A2 AC = 9 cm = 9×10-2 m
h = 6 mm = 6×10-3 m r = 7.5 cm = 7.5×10-2 m

Moving Electric Charge in a Magnetic Field. Lorentz Force.


Pic. 1

Introduction:

These demonstrations are based on a Double Beam Teltron Tube [Pic 1] and two different configurations of Helmholtz Coils. We only use a vertical electron gun with a deflector. The deflector changes the angle with which the electron beam enters the magnetic field. The setup shown in Pic 2 is used for all demonstrations.

When ordering please specify which part (1, 2, or 3) you would like to demonstrate.



Pic. 2


Pic. 4

Pic. 3

Part 1 - Spiralling Electrons

Setup the Helmholtz coils as show in Pic 3 and connect them in parallel.
Set voltages:

Set current in the Helmholtz coils IH to 1 A. Watch for the current in the tube, it should NOT EXCEED 20mA .

Students will see a spiraling electron beam up to 3 or 4 loops [Pic 4]. Instructor can play with the parameters of Lorentz formula by decreasing anode voltage, decreasing or increasing current through the Helmholtz coils, or changing the angle between the electron beam and the magnetic field by changing the potential of the deflector.



Pic. 6

Pic. 5

Part 2 - Determination of the e/m ratio

To find the e/m ratio, use the configuration of the Helmholtz coils shown in Pic 5.
Set voltages:

Set the total current in the Helmholtz coils IH to 0.5A. Again, watch for the current in the tube, it should NOT EXCEED 20mA.

Tune the current IH in coils and the deflector potential until a perfect circle will be achieved [Pic 6]. Measure the diameter (2R ≈ 8.5cm) of the circling electron beam with a caliper and record the value of the Helmholtz current IH. By using two simple equations for both the forces: evB= mv²/R and the energy: eVA = mv²/2, we can obtain the formula for e/m:



Pic. 7

Part 3 - Van Allen Radiation Belts

This is a demonstration for an astrophysics course, which simulates the Van Allen Radiation Belts [Pic.7 ]. The setup is the same that is used for spiraling electrons (Pic.3). Protons and electrons (the inner and the outer belts) are trapped in the Earth's magnetic field and travel back and forth in helical paths around magnetic field lines between the North and South magnetic poles. To show deflection of charged particles from the Earth back to the space, instructor should use a strong magnet in his/her hand which can deflect the electron beam back to the cathode.