PHYS 2426 Engineering Physics II EXPERIMENT 8 MEASUREMENT OF (e/m) FOR ELECTRONS I. OBJECTIVE The objective of this experiment is to measure the charge to mass ratio, (e/m), of the elec- tron. This will be done by using a special (e/m) apparatus which consists of an electron tube and a set of Helmholtz coils. The student will directly measure the accelerating volt- age, V, the coil current, I and the radius of the electron beam path, r. The calculated value of (e/m) will be compared with the accepted value. II. APPARATUS (e/m) apparatus, 2 power supplies, 2 multimeters and connecting wires. III. THEORY 1. The electron was discovered by the British physicist Sir J. J. Thomson (1856 - 1940) in the year 1897. Its charge and mass have the accepted values (four significant figures) e = 1.602 x 10-19 C and m = 9.109 x 10-31 kg. Thus the accepted value of the charge to mass ratio is (e/m) = 1.759 x 101 C/kg (1) 2. In the apparatus of this experiment, as the electron travels from the cathode to the anode, it is accelerated through a potential difference V. Thus its potential energy decreases by an amout eV and its kinetic energy increases by the same amount. This can be written as ev = =my?. (2) 3. The magnetic field of the Helmholtz coils exerts a force on the electron F = ev x B. This force bends the electron beam into a circle of radius mu r = - (3) eB Solving equations (2) and (3) for (e/m) (notice v is velocity and V is voltage) gives e 2V B272 (4) m 4. In this experiment, you will directly measure the accelerating voltage, V, the radius of the electron path, r, and the coil current, I. From the current, the magnetic field will be calculated using equation (5), then e/m will be calculated from equation (4).\f8. Calculate the relative uncertainty in B from the recorded uncertainty of I and Rcoil for one of the data points. 9. Extra Credit: Derive the expression for the magnetic field of a Helmholtz coil. This is equation (5). Hint: The magnetic field of a current loop at point P on the axis of the loop at a distance y from the plane of the loop is given by equation (12.15) in your textbook