Magnetism Question - Compare Radii of Circular Paths

[cmantzioros]

[SOLVED] Magnetism question

Homework Statement

A proton, a deuteron and an alpha particle with the same kinetic energies enter a region of uniform magnetic field, moving at right angles to B. Compare the radii of their circular paths.

Homework Equations

v = qBR / m

The Attempt at a Solution

Using the equation above:
K (kinetic energy) = [(q^2)(B^2)(R^2)] / 2m
so (R^2) = (2mK) / [(q^2)(B^2)]
From here, I don't know what to do... How do I compare the radii?

 

[cmantzioros]

Never mind... got it.

 

[ogb p]

The radii of the circular paths can be compared by looking at the values of R^2 for each particle. Since we are assuming that the kinetic energies (K) and the magnetic field strength (B) are the same for all three particles, the only varying factors are the mass (m) and charge (q) of the particles.

From the equation, we can see that the radius (R) is inversely proportional to the mass (m) and directly proportional to the charge (q). This means that the particle with the smallest mass will have the largest radius, and the particle with the largest charge will also have the largest radius.

In this case, the proton has the smallest mass and the largest charge, so it will have the largest radius. The deuteron has a larger mass than the proton, but a smaller charge, so its radius will be smaller than the proton's. The alpha particle has the largest mass, but the smallest charge, so it will have the smallest radius of the three particles.

Therefore, the order of the radii from largest to smallest is: proton, deuteron, alpha particle.