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.