1. Well, well, well, looks like we have a magnet and a particle caught in a magnetic field tango! Now, when the magnet moves, it creates a changing magnetic field, which will induce an electric field. This electric field will then exert a force on our particle, causing it to move.
Now, since the magnet has a velocity perpendicular to the magnetic field, that means the magnetic force experienced by the particle will be perpendicular to both the velocity of the magnet and the magnetic field. We call this a "slap-in-the-face" force!
Since we have a particle with mass m and charge Q, we can use the good ol' equation F = Q(v × B), where v is the velocity of the particle and B is the magnetic field. Remember, the force is perpendicular to both!
2. Alright, let's talk about the initial force when the particle is at rest. In the reference frame where the particle is initially at rest, we can remove its velocity element (since it's zero!) and we are left with F = Q(0 × B), which simplifies to F = 0.
Yes, you heard it right, my friend! The initial force on the particle is zero! It's like the particle is saying, "Hey, magnet, nice try, but I'm not budging!"
3. Now, let's hop into the reference frame where the magnet is at rest. In this scenario, we're moving with the magnet, so its velocity is zero in our frame. Now the equation becomes F = Q(v × B), but since v (the velocity of the particle) is zero in our frame, the force will still be zero!
That's right, folks! In the reference frame where the magnet is at rest, the initial force on the particle is still zero. It's like a superhero showdown with a lot of fancy moves, but no actual punches!
So, my friend, to sum it up:
1. The velocity of the particle a long time after the magnetic field has passed will depend on all the forces acting on it. We can't say for certain without more information.
2. The initial force on the particle in the frame where it is initially at rest is zero.
3. The initial force on the particle in the frame where the magnet is at rest is also zero.
I hope I didn't magnetize your brain with all the magnetic mumbo jumbo! If you have any more questions, feel free to ask!