- #1
gabdolce
- 6
- 0
Hey all,
I was wondering if one of you could help me out with a debacle I'm having.
I'm having trouble reconciling what exactly happens between an orbiting tetherball and the separate scenario of a orbiting particulate charge.
With the particulate charge: you can, given the velocity and magnetic field magnitude, determine the radius of the orbit of the charged particle.
F=ma=mv^2/r=qvB
r=mv/qB
In the case of varying B-field magnitudes, the only thing that changes is the radius of the orbit . The magnetic force is ALWAYS perpendicular to the velocity vector and thus can NEVER do work and NEVER (de)accelerate the spinning particle. Velocity of this particle must remain constant when the only perturbation can be altering the strength of the magnetic field.
Here is my confusion: As far as I can see, there is NO net torque on the system, therefore, there must be conservation of angular momentum.
Let's consider an INCREASING B field magnitude: According to L=mvr, since r is consequently getting smaller, shouldn't the velocity of this particle be increasing as well??
This would make sense, especially since when looking at a combination of F=mv^2/r and mvr, you get F=L/r^3 which further corroborates that the centripetal force here is getting larger (as we expected from the increasing of B)...
Is anyone else confused by this as well?
--------
Let's now look at a mechanical scenario: a tetherball circling the pole and getting shorter and shorter.
Can I use the conservation of angular here too and say that since the radius of orbit is getting shorter and shorter, then the tetherball must also be accelerating as well?
Thanks in advance.
I was wondering if one of you could help me out with a debacle I'm having.
I'm having trouble reconciling what exactly happens between an orbiting tetherball and the separate scenario of a orbiting particulate charge.
With the particulate charge: you can, given the velocity and magnetic field magnitude, determine the radius of the orbit of the charged particle.
F=ma=mv^2/r=qvB
r=mv/qB
In the case of varying B-field magnitudes, the only thing that changes is the radius of the orbit . The magnetic force is ALWAYS perpendicular to the velocity vector and thus can NEVER do work and NEVER (de)accelerate the spinning particle. Velocity of this particle must remain constant when the only perturbation can be altering the strength of the magnetic field.
Here is my confusion: As far as I can see, there is NO net torque on the system, therefore, there must be conservation of angular momentum.
Let's consider an INCREASING B field magnitude: According to L=mvr, since r is consequently getting smaller, shouldn't the velocity of this particle be increasing as well??
This would make sense, especially since when looking at a combination of F=mv^2/r and mvr, you get F=L/r^3 which further corroborates that the centripetal force here is getting larger (as we expected from the increasing of B)...
Is anyone else confused by this as well?
--------
Let's now look at a mechanical scenario: a tetherball circling the pole and getting shorter and shorter.
Can I use the conservation of angular here too and say that since the radius of orbit is getting shorter and shorter, then the tetherball must also be accelerating as well?
Thanks in advance.