PURPOSE

To measure the charge-to-mass ratio (e/m) for an electron and observe the effect of the magnetic force on a charged particle.

EQUIPMENT   Helmholtz coils, electron gun tube, filament supply, plate supply (50 V and 0.5 A), grid supply (0 to +5 V), Helmholtz coil supply (5 A), voltmeter, ammeter, half-meter stick.

RELEVANT EQUATIONS

Magnetic Force on Electron
Helmholtz Pair Field
Charge-to-Mass Ratio

DISCUSSION

The apparatus consists of two main parts: an electron gun tube to produce a beam of electrons, and a pair of Helmholtz coils to produce a uniform magnetic field at right angles to the electron beam in which the electrons travel.

The electron gun in the e/m tube consists of an indirectly heated cathode to supply the electrons; a grid, positively charged with respect to the cathode, to focus the electron beam; and a circular positively charged plate, which accelerates the electrons by imposing a positive potential difference V on them. The electron beam emerges vertically upward along the centerline of the tube through the center of a horizontally mounted disk (not the accelerating plate). Four circles marked on this disk have their centers at the hole through which the electrons emerge and have radii of 0.50, 1.0, 1.5, and 2.0 cm. The circles on the disk are coated with a substance that glows when struck by electrons. The tube contains a trace of an inert gas to make the path of the electrons (the beam) visible.

CAUTION!!! The life of the expensive tube is limited, so the tube should be operated at the lowest filament current and plate voltage to give a well focused beam. The plate voltage should never be turned on until after the filament is hot. The filament current should not exceed 0.55 amp. The plate voltage should not exceed 50 volts. The grid voltage must be positive and normally will be only a few volts, say under +5 volts with respect to ground.

The Helmholtz coils have their aluminum rings milled away at opposite ends of a diameter to allow the measurement of the average diameter. The number of turns per coil is marked on the equipment, and varies from one unit to another. The maximum current these coils can take is 4.70 amperes. In the course of the experiment, do not exceed this value! When the current is correct, the electron beam will be forced into a semicircle above the disk in the tube and strike one of the four circles on the disk. The diameter of the semicircle formed by the electron beam will then be the radius of the circle marked on the horizontal disk. The magnetic field strength, B, at the center point between the two Helmholtz coils is given by:

(1)

where is a universal constant equal to 4π x 10^-7 Wb/A-m, N is the number of turns per coil, I is the current in the coils (amperes), and R is the average radius of the coil (meters).

The magnetic force on an electron moving with velocity v perpendicular to B is discussed in the textbook where it is shown that the subsequent motion will be circular. If you do the calculations outlined in the Prelab Questions, you will produce an equation for e/m, which involves only the electric plate potential, V, the value of the magnetic field, B, the radius of the electron's path, r, and natural constants. These quantities are measurable and will allow you to determine e/m.