Notes for E/M experiment. Day one.

Motion of electrons in an electric field

Effects of changing current

The electron beam is a straight line because the magnetic field is in the same direction as the electron beam.

The electron beam becomes a spiral because the magnetic field is not along the same direction, nor perpendicular, to the electron beam. Rather, it is at some other angle which causes the electron beam to spiral.

Effects of changing voltage

Increasing the acceleration voltage decreases the angle of deflection, whereas increasing the deflection voltage increases the angle of deflection

Measurements

The 90 degree is at $80 \pm 2.5$ degrees. This measurement gives a circle of electron beams moving clockwise.

The readings on the ruler were taken by lining up the image in the mirror and the electron beam for one side of the beam and then again for the opposite side of the beam. This helps eliminate parallax.

Note that larger diameters are easier to interpret and gave a more accurate calculation of the e/m value.

Uncertainty

Calculations and values

$V_a= \pm 5V$

$I =\pm 0.005$, based upon accuracy recorded for the device readout $\Delta_2= \Delta_1 = 0.05$ $r\pm \Delta r = (d_2 \pm \Delta_2) - (d_1 \pm \Delta_1)$; $\Delta r =\sqrt{\Delta_1^2 + \Delta_2^2}$

Relative uncertainty for the e/m calculation:

$\frac{\Delta \frac{e}{m}}{\frac{e}{m}} = \sqrt{\frac{\Delta V}{V}^2 + 2\frac{\Delta R}{R}^2 + 2\frac{\Delta I}{I}^2}$

e/m $\pm \Delta$ e/m will be given by multiply our best estimate of e/m by the relative uncertainty

Sources

Electron beam starts at 100 V, voltage maxes at 300 V, current maxes at 3 A, and a minimum current is needed for a loop to exist.

Minor adjustments were made during the taking of data to keep the electron beam in a loop formation.