Question

3. Fill the blanks and the Proof - J.J. Thomson's experiment to fine the charge-to-mass ratio of the tt) (25 points) electron (i.e. e/m; The first is the experiment of Joseph John Thomson, who first demonstrated that atoms are actually composed of aggregates of charged particles. Prior to his work, it was believed that atoms were the fundamental building blocks of matter. The first evidence contrary to this notion came when people began studying the properties of atoms in large electric fields. If a gas sample is introduced into the region between two charged plates, a current flow can be observed, suggesting that the atoms have been broken down into charged constituents. The source of these charged particles is a heated cathode that, in fact, causes the atoms of the sample to ionize. These were known as cathode rays. In 1897, Thomson set out to prove that the cathode rays produced from the cathode were actually a stream of negatively charged particles called electrons. A schematic of the experimental setup is shown in Fig. 1 Step 1:determine v (the speed of moving charge particle, i.e. electron in this case) High voltage is applied between Cathode ( and Slits ( to make electrons accelerate from the cathode to the slits. Higer voltage makes faster acceleration and faster velocity in x-direction of the electron. Note that electrons only accelerate between the cathode and the slits After passing throgh the slits, electeons move in a constant velocity v owning to no friction in CRT (vacuum). Due to the electric field and the magnetic field made by the deflection plate and the magnetic field coils, the degree of electrons' deflection (T)will be affected by electron's velocity Therefore, given the known electric E and magnetic field B, we can change voltage V. across Cathode and Slits so as to change velocity v letting electron pass through the electric and magnetic field without deflection. We now zero in on the field region and set up a coordinate system as shown in Fig. 2. In this coordinate system, electrons enter the region between the plates with an (unknown) velocity v in the x-direction. In order to determine this velocity, electric and magnetic fields are both applied, and each gives rise to a force on the electron. These forces are in the y-direction. The electric in Fig. 2. In this coordinate system, electrons enter the region between the plates with an (unknown) velocity v in thex-direction. In order to determine this velocity, electric and magnetic fields are both applied, and each gives rise to a force on the electron. These forces are in the y-direction. The electric force | F (3 points) toward (ty or -y, 2 points), where E is the magnitude of the electric field, and e is electron. The magnetic force is | F,l (3 points) toward (ty or -y, 2 points), where B is the magnitude of the magnetic field. If these forces balance (i.e. | FHF ), then there will be no deflection () of the electron in y-direction, i.e. all of the electrons' motion will be along the x-direction, which was the initial direction when they entered the field region. If the forces balance, then the total force on the is | F-F0. Hence, the unknown velocity v can be determined as electrons will be zero, that (in terms of the electric field E and the magnetic field B, 5 points) Step 2: find the charge-to-mass ratio of the electron given the determine v from Step 1 Next, the magnetic field is switched off, so that the total force is due entirely to the electric field. Since the force is non-zero, if the charge carriers can be deflected ( by the force, this are fundamental charged particles provides evidence for their being fundamental particles. If they then they should have a well-defined mass and charge. In this second part of the experiment, the specific trajectory followed by the particle will be used to determine the ratio of the charge to the mass of the particle. When there is only an electric field, then there is a nonzero force | Fin the y-direction but no force in the x-direction. Thus, this problem is exactly the same as that of a projectile ( in a y-motion of the electrons can be analyzed separately and independently gravitational field. As can be done in the projectile problem, the x- and In the x-direction, the motion is very simple because there is no force in this direction. The electrons simply move with a constant velocity v, which we already determined in step 1. This value as a function of time t, the x-position has not changed. Thus, is x(t)vt of the electrons (in terms of the electric field E, the magnetic field B, and time t, 2 points) The force in the y-direction is a constant, hence motion in the y-direction is analogous the gravitational force. The constant force F gives rise to an acceleration aFe|/m where m is the mass of electron, and the y-position at time t is then y(t)at 2 The electric field is tuned such that the particle traverses the entire plate region in the time required for it to strike the positive plate. Let the total y-distance travelled be s, as shown in Fig. 2 The time T required to traverse the plate region (i.e. x(T)=v-T =l and =s) is 2 2S 2s / T = V 2 qUB=ma evB=ma m Prove that the charge-to-mass ratio of the electron (i.e. e/m; fjAIL) is V= 2sE elm= (5 points)

Answer 1

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