Hello, I'm having trouble understanding the answer of circular motion to this question. Any clarification would be appreciated!
Q: The mass spectrometer is used to determine the mass of particles. It operates by projecting particles, with known charge and velocity, through an evacuated chamber into a region of uniform magnetic field acting perpendicular to the velocity of the particles. Explain how the charged particles will behave as they enter the magnetic field and describe how this behaviour allows the mass to be determined.
Thanks!
Hey!
Let's start by thinking about what is actually going on in your scenario. We have a charged particle, fired into an area with a constant magnetic field. This means that, by the right hand rule, there will be a force acting on the particle. An example of this is displayed in the image.

However, remember that the force acting on the particle is CONSTANT (as it is proportional to the magnetic field, and the charge of the particle, neither of which are changing). Recalling the formula

We can see that if the force is constant, and the mass is constant, there will also be a constant acceleration! This means that the particle is 'rotating' through the field at the same, constant rate. The curve, therefore, will be uniform, and therefore traces out a circular path! See the image below for clearer details.

You can use the right hand rule along the entire path of the particle (just move your hand as though it IS the particle) to show that the force will always be towards the centre of the circle (ie. it is always accelerating towards the centre). If the circle is entirely contained within the magnetic field, it will trace the following path.

Okay great, so we know that the particle follows a curved path, accelerating towards the centre only. This sounds pretty familiar! Space shuttles, and orbits, work exactly the same way! So we can apply formulas used in the Space section here!
The next derivation is similar to the method used by JJ Thompson to figure out the mass:charge ratio of electrons. It's important to know the derivation for the HSC, although very few questions ask about it.
We know that the force acting on a moving charge in a uniform magnetic field is

However, we also know the force exerted on an object in orbit. The formula for centripetal force is

Since these two forces must be the same, we can equate them!


Since we know the charge, velocity and Magnetic field strength, and we can measure the radius of the spinning charge, we can figure out the mass!
Very rarely, HSC questions will make you derive things like this. You just need to think about what is actually HAPPENING, and try work things out from there. I hope that this explanation helped! Let me know if I can clarify anything.
Jake