Magnetism Question - Compare Radii of Circular Paths

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In a uniform magnetic field, the radius of circular paths for charged particles is determined by their mass, charge, and kinetic energy. The relationship is expressed by the equation R = (2mK) / (q^2B^2), where R is the radius, m is mass, q is charge, and K is kinetic energy. For a proton, deuteron, and alpha particle with identical kinetic energies, the differing masses and charges lead to variations in their radii. The alpha particle, being the heaviest and having the highest charge, will have the smallest radius, while the proton will have the largest. This comparison illustrates how mass and charge influence the motion of charged particles in magnetic fields.
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[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?
 
Last edited:
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Never mind... got it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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