Magnetic field affecting an alpha and a beta particle.

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SUMMARY

The discussion focuses on calculating the ratio of the radii of the paths of an alpha particle and a beta particle moving through a uniform magnetic field. The relevant equation for the radius of the path is given by r = mv/BQ, where m is mass, v is velocity, B is magnetic field strength, and Q is charge. The mass of the alpha particle is approximately 1840 times greater than that of the beta particle, while the charges are +4e for the alpha particle and -e for the beta particle. The conclusion is that the radius of the path of the alpha particle will be significantly larger than that of the beta particle due to its greater mass and positive charge.

PREREQUISITES
  • Understanding of magnetic fields and their effects on charged particles.
  • Familiarity with the equation r = mv/BQ for circular motion in magnetic fields.
  • Knowledge of the properties of alpha and beta particles, including mass and charge.
  • Basic physics concepts related to particle motion and forces.
NEXT STEPS
  • Research the derivation and applications of the equation r = mv/BQ in different contexts.
  • Study the differences in mass and charge between various subatomic particles.
  • Explore the effects of magnetic fields on charged particles in more complex scenarios.
  • Learn about the experimental methods used to measure particle trajectories in magnetic fields.
USEFUL FOR

Students studying physics, particularly those focusing on electromagnetism and particle physics, as well as educators looking for practical examples of magnetic field interactions with charged particles.

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Homework Statement


An \alpha-particle and a β-particle are both traveling along the same path at a speed of 1.5x106 ms-1.

They then enter a region of uniform magnetic field. The field is a square with sides of 1 cm.

The magnetic field is normal to the path of the particles and is into the plane of the paper.

Calculate the ratio 'radius of the path of the alpha particle/radius of the path of the beta particle.'



2. The attempt at a solution

I don't even know how to start thinking about this question. I mean I know that the radius of the alpha particle will be greater than that of the beta particle because of their differences in mass and charge but how do you do go about that in fractions?
 
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Hint: What are the relevant equations and how would they differ for α/β particles?
 
r = mv/BQ? no?

For an α-particle, m would be (1840x4) times greater than for a β-particle [because it's a helium nucleus and a β-particle is an electron]. v is the same for both particles. B is also the same. Q, the charge, on the other hand, will be positive and negative for alpha and beta respectively, with values [if they're needed in the first place] of +4e and -e for alpha and beta respectively. I hope I'm right with all that data.

Here's what's bothering me. What do I do with this to answer the question? I mean how do I use it?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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