Uniform magnetic field - charge on particle changes So the problem in my study guide is as follows: "If a particle of charge $q$ travels in a circular path in a uniform magnetic field of 2T and suddenly the charge is replaced by $2q$, what is the new value of its radius?"
The solution uses the fact that net (centripedal) force is equal to magnetic force, so
$\frac{mv^2}{r}=qvB$, thus $r=\frac{mv}{qB}$.  Since charge is doubled, radius is halved.
My question is how we're supposed to know that the speed of the particle doesn't change.  This seems to be a key part of solving the problem, but the solution says nothing about it.  Is there a reason why this is, or is the problem just ill-defined (that is, not enough information was included in the problem and they should have specified that speed is unchanging)?
 A: The question is why would it, there isn't any factor in the setup that might change the velocity $v$ of the particle if it was, by the context, "suddenly replaced". Of course base on conservation of momentum law, the velocity has to reduce to compensate for the added mass (if that's the case), but purely based on intuition, you'll know if a variable as sensitive as velocity of the particle changes, you'll be well aware and informed in the question. More charge in either positive or negative direction means less or more electrons available respectively. Electron has mass, hence added or reduced electrons will increase or reduce the mass in the equation, hence the velocity has to compensate provided no energy is introduced or taken away from the system.
If you're the observant type, you'll notice that some physics questions just want to know what happens to a certain variable in a physical system provided everything else is kept constant even when it's unrealistic to do so. So I believe this might be one of those cases.
