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e-m Ratio Manual

# e-m Ratio Manual - Phys211L/Phys205L Measurement of charge...

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Phys211L/Phys205L Measurement of charge to mass ratio of electrons 1. Object : To determine the ratio of the charge to mass of an electron. 2. Equipment : Set of Helmholtz coils, cathode-ray tube, power supply, ammeter, voltmeter, variable resistors, transformers. 3. Theory : When a moving electron passes through a magnetic field, it is subjected to a magnetic force: F m = evB sinα Where B is the magnetic field, v is the velocity of the moving electron, e is the charge of the electron, and α is the angle between the direction of the magnetic field and the velocity. If the velocity and the magnetic field are perpendicular, then the expression of the force becomes: F m = evB (1) This force causes the electron to move in a circular orbit, the plane of which is pependicular to the magnetic field. The radius r of the circle is such that the required centripetal force is furnished by the above force. Therefore F m = evB=mv 2 /r (2) In which m is the mass of the electron. If the electron aquires its velocity by being accelerated through a potential difference V. Its kinetic energy is: ½ mv 2 =eV (3) Combining equations (2) and (3) gives e/m = 2V / (B 2 r 2 ) (4) Using this equation one can determine of the ratio of charge to mass of the electron if V, B, and r are known.

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