Physics307L:People/Ozaksut/E over m

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http://openwetware.org/wiki/Physics307L:People/Ozaksut/Notebook/071128

e/m

• e/m Lab Manual

Goal

• measure the charge to mass ratio of an electron
• understand EM

Theory

Electric currents induce magnetic fields. The magnetic field along the axis of symmetry generated by Helmholtz coils is given by an equation relating number of coils, current in the coils, and radius of the coils. Helmholtz coils are special because the magnetic field between them is nearly constant for a larger area than for other magnetic field inducing coils. We know the number of coils and radius of coils, and we will control the current in the coils using a power supply.

The magnetic field generated by a current in the counterclockwise direction will be parallel to the ground, in the direction of the experimenter. The force on a charged particle in the magnetic field will be qvXB, so any particle with initial velocity in the counterclockwise direction will continue to travel in a circle, in the counterclockwise direction, due to the force on the particle directed towards the center of the circle.

The centripetal force on the electron is ma=mv^2/r, and the centripetal force is equal to the force the electron feels from the field, we equate ma=mv^2/r=qvXB=qvB because v, B are perpendicular always. q/m=v/rB. now, r=mv/qB.

The kinetic energy of the electrons when they leave the electron gun is given by mv^2/2=qV. so the velocity is v=(2qV/m)^1/2. q/m=v^2/2V. v/rB=v^2/2V. v=2V/rB.

We will accelerate electrons off of an electron gun with different voltages between Helmholtz coils and measure the radius of the circular path. With this information, we can calculate the ratio e/m.

theory http://www.physics.northwestern.edu/Lab/eoverm.pdf Northwestern's lab manual is a thorough guide to this lab.

Equipment

• Helmholtz coils
• three power supplies
• electron gun and helium bulb
• three multimeters

Setup

First, we connect banana plugs from a DC power supply (Soar Corporation DC Power Supply 7403) to the electron gun heater jacks on the e/m apparatus for 2 minutes at .7 A current, 6.3 V voltage. (Uchida e/m Experimental Apparatus Model TG-13)

Then, we turn on the 200V DC power supply (Gelman Instrument Company Deluxe Regulated Power Supply) and connect it with banana plugs to the electrode jacks on the apparatus at 200V, 25mA. The electrodes are what supply the accelerating voltage to the anode which pulls excited electrons from the cathode. We want to know the accelerating voltage precisely, so we connect a voltmeter (BK Precision Digital Multimeter 2831 B), to the Voltmeter sockets on the e/m Apparatus with banana plugs.

Finally, we turn on the coil current (Soar DC power Supply PS3630) connected in series through a multimeter (Wavetek True RMS 85 XT) to ensure accuracy in our calculations at 1.96 A and 8 V.

A mirrored ruler is mounted on the back of the Helmholtz coils so that measurements of the electron beam radius can be taken.

The Procedure

We take two data sets, once holding accelerating voltage constant and once holding coil current constant, and varying the other parameter.

Data

Please see the excel spreadsheet of our data and calculations here: