The Ratio of Charge to Mass (e/m) for an Electron

Transcription

1 The Ratio of Charge to Mass (e/m) for an Electron OBJECT: The object of this experiment is to determine the ratio of charge to mass (e/m) for an electron and compare it with its theoretical value. THEORY: When an electron moves with speed v perpendicular to a magnetic field of intensity B, a magnetic force F acts on the electron. The magnitude of this force is given by Where; e is the charge of an electron and v is the speed of electron F = B e v (1) The direction of this force is perpendicular to the direction of magnetic field and to the direction of motion of the electron. Since the magnetic force acting on the electron is always perpendicular the electron s direction of the motion, the electron will travel in a circular path of radius r. The centripetal force required to keep the electron moving in a circular path is supplied by the magnetic force acting on it. The expression for the required centripetal force is m v F = r () where; m is the mass of electron and r is the radius of electron s path. Equating equations (1) and () yields m v r = B e v (3) If we solve the Eq. (3) for the ratio of electronic charge to mass (e/m) we obtain e = m v B r (4) The velocity of the electron is yet known, but it can be found as follows. When an electron is accelerated through a potential difference V a (anode potential), the gain in its kinetic energy is equal to work done on the electron by the electric field. This work W is equal to V a e. Thus 1 W = V a e = mv (5) 1

2 Solving Eq. (5) for v yields v = V e/m a (6) Substituting Eq.(6) into Eq.(4) and solving for (e/m) one obtains e V = a m B r (7) Final equation will be used to find the experimental value for the ratio (e/m) for an electron in terms of the accelerating anode potential V a, the magnetic intensity B, and radius r of the circular path of the electron. EXPERIMENTAL DETERMINATION OF THE RATIO e/m FOR AN ELECTRON a) Calculation of B : The Helmholtz arrangement for the production of homogeonus magnetic field is characterized in that two indiviual circular conductors of equal radius the centers of which are in the common axis and have a distances equal to the radius of the conductors carry same current. The magnetic induction of B in the central region of such a Helmholtz- coil system may be calculated from the mean radius of the coils R (0,068 m), the number of turns n (30) of one coil and the current I B (A), µ n 0 B = IB R Volt sec m ( Tesla = ) (8) where µ 0=1.56*10-6 (Volt sec/a.m.). To calculate the magnetic field intensity,the current I B (flowing through both coils) must be introduced; it is assumed that the current in both coils equal. It is noted that the start of each coil is connected to the four 4 mm socket (A) on the side of the bobbin, and the finish to the 4 mm socket (Z). For a normal connected series Helmholtz arrangement, the power supply should be connected to sockets (A), with sockets Z interconnected.

3 Experimental set-up: Connect the deflection tube in to the circuit shown below, with both deflecting plates at anode potential; Switch on and observe the path of undeflected beam. Figure 1 Specification: Maximum filament voltage is 7.5 V Anode voltage V Typical operation V Anode current 1 ma Procedure: 1. Energise the Helmholtz coil and observe, with reference to the screen that a. the radius (r) decreases with the increase coil current I B at fixed V a values, b. the radius (r) increase with increase in anode potential V a, indicating a higher electron beam velocity, with fixed I B Explain the reasons of above observations.. At different fixed values of V a,calculate the value of B as a function of the coil current I B using Eq.(8) and measure each corresponding radius (r). Determine the value of (e/m) by plotting the graph of 1/r versus B /V a (see Eq.7). The slope of the graph gives (e/m) wheree V a is fixed. 3. Repeat the previous calculations by, this time, plotting V a against the B r for various anode potentials at fixed B value. The slope of the graph gives (e/m). Compare the previous and present obtained (e/m) values. 4. Calculate the theoretical value of ratio (e/m) for an electron by dividing the theoretical value of its mass. 5. Determine the percentagee error in your experimental result by comparing the obtained experimental value of (e/m) with its theoretical value, and list the possible errorr sources. 3

4 Questions: 1. What is the reason behind the experimental determination of (e/m) value?. If the earth s magnetic field were used to deflect an electron beam, calculate the smallest possible diameter of the required tube. Assume that the accelarating potential difference is the same as that used here. 3. Could the coil power be an AC source? Explain your answer in detail. 4. What experimental differences, if any, would result if the tube produced a beam of protons rather than electrons? Prelab Questions 1. Who discovered the electron and when?. What is the electron? (charge, mass. etc) 3. What is the proton and neutron? (charge, mass etc) 4. What is the magnetic field? How can electron move in magnetic field? Is electron energy change with applied magnetic field? 5. What is the world s magnetic field? 6. What is the electric field? How can electron move in electric field? Is electron energy change with applied electric field? 7. How can you produce homogeneous magnetic field? 4

5 ATTENTION!!! You have to solve pre-lab questions before the experiment. You should visit web sites belows for other resources; (Turkish) For calculations, you need to use least square fitting method to obtain the (e/m) slope. You may find useful informations on following webpages or you can use Exprimental Physics(EP 371) lecture notes. Res.Assist Ebru BAKIR Res.Assist Haydar MUTAF 5