Charge to Mass Ratio of the Electron

Charge to Mass Ratio of the Electron - Charge to Mass Ratio...

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Charge to Mass Ratio of the Electron Akshaya Annavajhala Department of Physics, Case Western Reserve University Cleveland, OH 44016 Abstract: Filler Introduction and Theory: Using a potential difference and a hot filament in a vacuum tube, one can create free electrons in the tube that are accelerated due to the potential difference. These electrons gain a potential energy 2 1 2 eV mv = . Using a magnetic field, we can steer these electrons due to the fact that an electron feels a force ( ) F e v B = - u u v v v . As is clear from the equation, the cross product shows that the force must be perpendicular to both velocity and the magnetic field. This force must then clearly force the electron into a circular motion, as circular motion is derived from the constant perpendicularity of acceleration and velocity. Hence, we can use the magnitude of the force ( evB from (1.2)) in Newton’s well-known Second Law as follows: 2 mv evB R = . The cancellation of one velocity factor and the readjustment of the resultant equation along with equation (1.1) provide us with the equation for the ratio of the charge of the electron to its mass: 2 2 ( ) e V m BR = . This is clearly a good sign, as the lab’s objective is to determine the mass of an electron. Although the above equation provides only a ratio, independent experiments have established the value of e for us. Our expected ratio (according to CODATA) is 11 1.76 10 e C m kg V , disregarding the small error for now. The entire experiment depends on the magnetic coils’ resultant field, which is described by the relationship 0 8 5 5 c NI B r μ = ,
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where the all of the factors are constant for our experiment but one: I c , which is the current in the coils. This equation can be used with equation (1.4) to remove the value of B: 2 2 2 0 2 8 5 5 c e V m N I R r μ = . Moving R (radius) to the left and inverting the equation gives us a linear relationship between the inverse of R and I c , with the slope equal to 0 8 / 5 10 N e m r V , as is seen from equation (1.7). Another rearrangement of equation (1.7) relates R and the
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This note was uploaded on 05/09/2008 for the course PHYS 124 taught by Professor Starkman during the Spring '08 term at Case Western.

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Charge to Mass Ratio of the Electron - Charge to Mass Ratio...

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