Electromagnetism in Objective-C

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26 Electromagnetism
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The electric and magnetic fields could be adjusted until the beam of electrons followed a straight, or undeflected, path When this occurred, the forces due to the two fields were equal in magnitude and opposite in direction Mathematically, this can be represented as follows: Bqv
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Eq Bq
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Solving this equation for v yields the following expression: v
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This equation shows that the forces are balanced only for electrons that have a specific velocity, v If the electric field is turned off, only the force due to the magnetic field remains The magnetic force is perpendicular to the direction of motion of the electrons, causing them to undergo centripetal (center-directed) acceleration The accelerating electrons follow a circular path of radius r Using Newton s second law of motion, the following equation can be written to describe the electron s path: Bqv
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Solving for q/m results in the following equation
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q v m Br In a Thomson tube, the ratio of an electron s charge to its mass is equal to the ratio of the electron s velocity divided by the product of the magnetic field strength and the radius of the electron s circular path
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Charge-to-Mass Ratio in a Thomson Tube
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Thomson calculated the straight trajectory velocity, v, using measured values of E and B Next, he measured the distance between the spot formed by the undeflected beam and the spot formed when the magnetic field acted on the beam Using this distance, he calculated the radius of the electron s circular path, r Knowing the value of r, Thomson was able to calculate q/m By averaging many experimental trials, he determined that q/m 1759 1011 C/kg Using this value for q/m and the known value of q, the mass of the electron (m) was calculated m
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q q/m 1602 10 19 C 1759 1011 C/kg
Figure 26-2 This photograph shows the circular tracks of electrons (e ) and positrons (e ) moving through the magnetic field in a bubble chamber, a type of particle detector used in the early years of high-energy physics Electrons and positrons curve in opposite directions
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Thomson s experiments with protons Thomson also used his cathoderay test apparatus to determine the charge-to-mass ratio for positive ions He took advantage of the fact that positively charged particles undergo the opposite deflection experienced by electrons moving through an electric or magnetic field The differing deflection of electrons and positive ions can be seen in Figure 26-2 To accelerate positively charged particles into the deflection region, Thomson reversed the direction of the electric field between the cathode and anodes He also added a small amount of hydrogen gas to the tube The electric field pulled electrons off the hydrogen atoms, changing the atoms into positive ions These positive hydrogen ions, or protons, were then accelerated through a tiny slit in the anode The resulting proton beam passed through electric and magnetic fields on its way toward the end of the tube
Section 261 Interactions of Electric and Magnetic Fields and Matter
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Using this technique, the mass of a proton was determined in the same manner as was the mass of the electron The mass of a proton was found to be 167 10 27 kg Thomson went on to use this technique to determine the masses of heavier ions produced when electrons were stripped from gases, such as helium, neon, and argon
Path Radius An electron with a mass of 91 10 31 kg moves through a cathode-ray tube at 1 20 105 m/s perpendicular to a magnetic field of 35 10 2 T The electric field is turned off What is the radius of the circular path that is followed by the electron
Analyze and Sketch the Problem
Draw the path of the electron and label the velocity, v Sketch the magnetic field perpendicular to the velocity Diagram the force acting on the electron Add the radius of the electron s path to your sketch Known:
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