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Calculation of charge-to-mass ratio is of great importance when it comes to the subject of Modern Physics. Understanding the procedure behind this experiment is equivalent to revising the following topics as well :
- Moving charge in Magnetic Field
- Behaviour of Charge in Electric Field
- Projectile Motion
Sections :
- Importance of calculating e/m ratio
- Setup of the experiment
- Procedure (*Imp)
- Final Data & Conclusion
1. Importance of e/m Ratio
Ok, so you have a value called e/m ratio ! But why is it important to caluculate this value? Is there any applications of it ?
- In simple words, the charge-to-mass ratio of a charge helps us to predict the behaviour of the particle under electric and magnetic fields. This ability to predict the particles behaviour enables us to have an idea of adjusting the setup in order to have so and so outcomes.
We can see it’s application in :
Electron Microscopes :
- Electron Microscopes are known for their ability to magnify the images to a very high resolution & this is done with the help of a beam of electrons
- Knowing the e/m ratio enables the scientists to control the movement of electrons and a result, they produce the required resolution of the image
Particle Accelerometers :
- These are used in order to accelerate the charged particles.
- By knowing the charge-to-mass ratios, we can actually control the trajectories of the particles.
2. Setup of the Experiment
The Setup mainly consists of the following things :
- Filament F
- Battery V
- Pump
- 2 parallel plates, across which another battery has been connected
- Current carrying coil wire (not shown in setup)
- Screen S
Fig. Setup for the Experiement
Purpose :
- Filament F : The filament is inclusive of that battery (not V) shown in figure.
- Voltage V :
– The plate attached to the positive terminal is used as anode to attract the electron cloud. This is done to make the electrons accelerate.
– Each electron has different energies when they come out from atoms. And when they are accelerated due to potential difference of V, then they all end having different set of velocities.
- Pump : To create vacuum inside the tube
- The parallel plates kept facing each other + battery setup, is used to create a uniform electric field E in the region between the two plates. Direction will be from positive plate to negative plate
- Current carrying coil wire : This is done in order to setup a steady magnetic field B (going into the plane)
- Screen S : Whenever an electron strikes the screen S; it creates a spot on the screen which helps us to detect and hence analyze the trajectory/path taken by the electron.
Note that : The E and B vectors are perpendicular to each other
3. Procedure
Step-1 :
As discussed, the anode attracts the electron cloud which makes them to accelerate towards the screen S. But well before they reach the screen, the electrons are made to pass through a region R where, for now, only Electric field is applied (B is turned off).
The current setup for Step-1 looks like :
As the electrons pass through ‘Region R‘ , they undergo deflection ‘y’ due to the electric field and follow a trajectory as shown (green) . We zoom into the Region R to get a better understanding of what’s happening
Zoomed picture of Region R :
We need the expression for deflection ‘y’.
Important : Note that the deflection is going to be measured from axis
Some of the Projectile comes into picture now !
- This ‘y’ is measured during the experiment
Step-2 :
Now, our aim is to find the velocity ‘v’ of the electron. Recall that the ‘y’ is the deflection –> BUT Deflection from which path ? The answer is ‘the axis’ . We need to find the deflection caused in electron’s trajectory due to the electric field E because otherwise in the absence of E, it would just follow the straight path along axis.
- For getting the speed (v) of the electrons which go undeflected, we introduce B now in addition to E in order to make zero deflection. This is equivalent to saying that there was none of the fields present in region R
We have to balance the forces (to get zero deflection). Remember it’s a negative charge.
We then adjust the values of E and B until the magnitudes of forces are same. This allows us to build a ‘velocity selector‘
Velocity Selector :
As discussed in Section 2 of this article, all the electrons come with different set of velocities. But, for continuing our experiment, we need only the electrons of specific velocity to be focused on. So, how to exactly distinguish those electrons ?
We can clearly see the relation of E and B with velocity. This means that controlling the values of E and B allows us to select the electrons which have their velocities as E/B. The electrons possessing this specific velocity will go through the region undeflected and hence we can separate them.
Step-3 :
Calculating the e/m ratio with the expressions and equations we got till now :
Substituting v = E/B in the expression of y obtained in step-1, we get :
4. Final Data
Conclusion
- This completes our e/m calculation experiment performed by Sir J.J. Thomson.
- The article or the whole experiment procedure itself has a lot of concepts involved in it which makes it even more important to understand, both as an Experiment as well as an good multi-concept level problem
Keep Learning !
