What Is the Charge to Mass Ratio of a Mystery Particle in a Thomson Apparatus?

[hockeyhoser23]

Homework Statement

A mystery particle enters the region between the horizontal plates of a Thomson apparatus; its initial velocity is parallel to the surface of the plates. The separation of the plates is and the length of the plates is . When the potential difference between the plates is , the deflection angle of the particle (as it leaves the region between the plates) is measure to be 0.20 radians. If a perpendicular magnetic field of magnitude is applied simultaneously with the electric field, the mystery particle instead passes through the apparatus undeflected.

Find the charge to mass ratio for this particle.

It’s a common particle; identify it.

Find the horizontal speed with which the particle entered the region between the plates.

Homework Equations

f= ma
f=qE
qE=ma
E=V/d

The Attempt at a Solution

So I know that the deflection of the particle is proportional to its q/m ratio (because the deflection is inversely proportional to the mass of the particle from f=ma ). I have it down to a= E * q/m, I know the deflection in y = sin (theta). From here I'm not sure where to go, any help?

 

[Delphi51]

The idea here is that the electric force Fe cancels out the magnetic force Fm on the moving particle. You must begin by writing
Fe = Fm
Then fill in the detailed formula for each force and solve for the velocity of the particle.

Finding q/m is going to be more difficult. Without the magnetic field, the particle is deflected into 2 dimensional motion by the electric field. You know the angle and the horizontal distance, so you can figure out the vertical distance of the deflection. That should enable you to use the constant speed formula on the horizontal part and the accelerated motion formulas on the vertical part. Surely you will be able to deduce the acceleration from them so you can use your formula relating q/m to the acceleration.

 

[tomcue]

I would approach this problem by first identifying the known quantities and equations that can be used to solve for the unknowns. From the given information, we know the separation and length of the plates, the potential difference between the plates, the magnetic field strength, and the deflection angle of the particle. We also have equations relating force, electric field, and mass/charge ratio.

To solve for the charge to mass ratio of the particle, we can use the equation qE=ma. Rearranging this equation, we get q/m = a/E. We know the value of a from the deflection angle, and we can calculate the electric field E using the given potential difference and plate separation. Therefore, we can solve for the unknown q/m ratio.

To identify the particle, we can use the known values of the charge to mass ratio for different particles. By comparing the calculated value to these known values, we can determine the most likely identity of the mystery particle.

To find the horizontal speed of the particle, we can use the equation f=qvB, where f is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength. Since the particle is undeflected when the electric and magnetic fields are applied simultaneously, we can equate the electric and magnetic forces (qE= qvB) and solve for v. This will give us the horizontal speed of the particle as it enters the region between the plates.

In conclusion, by using the given information and relevant equations, we can solve for the charge to mass ratio, identify the particle, and find its initial horizontal speed. Further experimentation and analysis may be needed to confirm these results and provide a more comprehensive understanding of the mystery particle and its behavior.