chapter26

**Chapter 26: ** **The Magnetic Field **

**Background/General Information**  **Force Exerted By A Magnetic Field**
 * With information previously discovered by the Greeks (magnetite attracts pieces of iron), Pierre de Maricourt (1269) discovered that a needle on a natural spherical magnet orients itself along lines that pass through points on opposite ends of the sphere. He called the points "poles".
 * Other experimenters noted that every magnet (of any shape) has 2 poles where the force exerted by the magnet is strongest
 * Also noted that like poles of 2 magnets repel each other and unlike poles attract.
 * In 1600, William Gilbert discovers that the earth is a natural magnet with poles near the north and south geographic poles.
 * North pole of a compass needle points toward the south pole, thus it is actually a south magnetic pole
 * Magnetic Poles always occur in pairs.
 * When a magnet breaks, the result is 2 magnets. At the breakpoint, equal and opposite poles appear at either side.
 * (Moving Point Charge) When a charge //q// moves with velocity //v// in a magnetic field //**B**//, the magnetic force //**F**// is




 * The direction of forces exerted on charges moving in a magnetic field is determined by the Right-Hand Rule

<span style="color: #ffb200; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">
 * <span style="color: #ffb200; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Fingers in the direction of velocity (v)
 * <span style="color: #ffb200; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Curl fingers in direction of magnetic field (B)
 * <span style="color: #ffb200; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Thumb is pointing in direction of force (F)
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">SI unit of magnetic field is the tesla (T), however, the commonly used unit (not an SI unit) is the gauss (G).
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">(Current in a wire) When a wire carries a current in a magnetic field, there is a force on the wire that is equal to the sum of the magnetic forces on the charged particles whose motion produces the current
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">L points in same direction as I
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">RHR #1 - Fingers in direction of I, curl towards B, thumb is direction of F [for (+) current]
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">RHR #2 - Source of current
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">B can be represented by magnetic field lines, just like E can be represented by electric field lines.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Similarities - (1) direction of field indicated by direction of field lines, (2) magnitude of field is indicated by their density.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Differences - (1) E-field lines are in direction of the electric force on a positive charge, but magnetic field lines are perpendicular to the magnetic force on a moving charge. (2) E-field lines begin on (+) charges and end on (-) charges; Magnetic field lines neither begin nor end.

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">**Motion of a Point Charge in a Magnetic Field**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Magnetic force on a charged particle moving through a magnetic field is always perpendicular to the velocity of the particle.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Thus, magnetic force changes direction of velocity, but //not// its magnitude.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Magnetic fields do no work on particles and do no change to their kinetic energy.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">When particle moves in circular orbit, we can use Newton's Second Law to relate the radius of the circle to the magnetic field and speed of the particle:



<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">**Velocity Selector**
 * <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Region in which there is a uniform electric and magnetic field. They are perpendicular to one another, as well as to the initial velocity of the charged particles that are passing through the region.
 * <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Force exerted on a charged particle by the electric field:
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">//F = qE//
 * <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Magnitude of force exerted by magnetic field is....as long as the velocity is perpendicular to the field
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">//F = qvB//
 * <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">If 2 forces are equal and opposite, net force is zero. The particle passes through the region without changing direction.
 * <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">(With magnetic force being dependent) Any charges traveling faster/slower than the ones going straight through will be deflected.

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">**Thomson's Measurement of q/m for Electrons**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Experiment (1897) showed that the rays of a cathode-ray tube can be deflected by electric and magnetic fields.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Indicates that they must consist of charged particles
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">All particles have the same ratio q/m
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Ratio can be obtained using any material for a source
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Thus, these particles are a fundamental constituent of all matter
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">These particles are now called electrons

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">**The Mass Spectrometer**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Designed by Francis William Aston (1919)
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Measures the masses of isotopes
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Important in determining the presence of isotopes and their abundance in nature
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">The mass-to-charge ratio of an ion of known speed can be determined by measuring the radius of the circular path taken by the ion in a known magnetic field.

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 23px;">**The Cyclotron**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 23px;">Invented by E.O. Lawrence and M.S. Livingston (1934)
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 23px;">Accelerate particles (protons, deuterons) to high kinetic energies
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 23px;">High energy particles are used to bombard atomic nuclei, causing nuclear reactions that are used to study the nucleus

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 23px;">**Torques on Current Loops**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">﻿A current carrying loop does not experience a force in magnetic field, but a torque that tends to twist the loop.
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">Torque can be written in terms of magnetic dipole moment (aka magnetic moment) u
 * [[image:Equation_11.jpg width="94" height="24"]]
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">Torque on a current loop
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">[[image:Equation_12.jpg width="93" height="22"]]
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Work is done when a torque is exerted through an angle

<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Integrating... <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">PE of the dipole is... <span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">**The Hall Effect**
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Discovered by Edwin Hall (1879)
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">This is the production of a voltage difference across an electrical conductor
 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">When a conducting strip that carries a current is placed in a magnetic field, the magnetic force on the charge carriers cause a separation of charge called the Hall effect. The separation of charge results in a voltage called the Hall voltage


 * <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 16px; line-height: 23px;">Quantum Hall effects: measurements at very low temperatures in large magnetic fields show that the Hall resistance is quantized, thus only taking on values given by



<span style="color: #ffb200; font-family: 'Lucida Console',Monaco,monospace; font-size: 150%;">**Practice Problems**

<span style="color: #060689; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">A //flicker bulb// is a light bulb that has a long, thin flexible filament. It is meant to be plugged into an ac outlet that delivers current at a frequency of 60 Hz. There is a small permanent magnet inside the bulb. When the bulb is plugged in the filament oscillates back and forth. At what frequency does it oscillate?

<span style="color: #ff0000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Because the alternating current running through the filament is changing every 1/60 s, the filament <span style="color: #ff0000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">experiences a force that changes direction at the frequency of the current.

<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">A velocity selector has a magnetic field that has a magnitude equal to 0.28 T and is perpendicular to an electric field that has a magnitude equal to <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 15px; line-height: 27px;">0.46 MV/m. (//a//) What must the speed of a particle be for that particle to pass through the velocity selector undeflected? What kinetic energy must (//b//) protons and (//c//) electrons have in order to pass through the velocity selector undeflected?

<span style="color: #ff0000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">A.

<span style="color: #ff0000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">B. <span style="color: #ff0000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">C.

<span style="color: #060689; font-family: 'Lucida Console',Monaco,monospace; font-size: 260%;">**Laboratory:** <span style="color: #ffb200; font-family: 'Lucida Console',Monaco,monospace; font-size: 220%;">﻿The Magnetic Field in a Slinky

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Solenoids are used in electronic circuits or as electromagnets. In this lab we will explore factors that affect the magnetic field inside the solenoid and study how the field varies in different parts of the solenoid. A metal slinky will serve as our solenoid.

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Materials: <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Vernier computer interface <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Magnetic Field Sensor <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Slinky <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Switch <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Meter Stick <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-DC power supply <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Ammeter <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Connecting Wires (2 or 3) <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">-Tape

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 15px; line-height: 27px;">Set-up should look like this: <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 15px; line-height: 27px;">

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">Procedure: <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">1. Place the Magnetic Field Sensor between the turns of the Slinky near its center (as shown). <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">2. Close the switch and rotate the sensor so that the white dot points directly down the long axis of the solenoid. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">3. With the switch open, zero the sensor to remove any magnetism in the metal of the slinky or table. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">4. Adjust the power supply so that 0.5 A will flow through the coil when the switch is closed. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">5. Click collect to begin data collection. Close the switch for at least 10 seconds during the data collection. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">6. View the field vs. time graph and determine the region of the curve where the current was flowing in the wire. Select this region on the graph by dragging over it. Determine the average field strength while the current was on by clicking on the Statistics button. Record the average field in the data table. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">7. Increase the current by 0.5A and repeat steps 5 and 6. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">8. Repeat step 7 up to a maximum of 2.0 A. <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 32px;">9. Record length, turns, and number of turns per meter in the data table.

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">DATA TABLE <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;"> <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; line-height: 27px;"> <span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%; line-height: 27px;">Compass - Uses the earth's magnetic field. North and south poles
 * <span style="color: #060689; font-family: 'Lucida Console',Monaco,monospace; font-size: 150%; line-height: 27px;">﻿Real World Applications **

<span style="color: #343232; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 120%;">Radio Antennas - electric and magnetic fields

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 * CATEGORY ||  SCORE (1-4)  ||  POINTS (0-20)  ||
 * Content || 3.5 || 17.5 ||
 * Organization || 4 || 20 ||
 * Accuracy || 4 || 20 ||
 * Appearance || 4 || 20 ||
 * Participation || 4 || 20 ||
 * TOTAL || 97.5 ||