# Lenz's law for point charge in time varying magnetic field?

1. Oct 15, 2012

### cfitzU2

Hello friends,

So I have a point charge with mass m and charge +e entering a uniform magnetic field B at velocity v from the "right". The field is perp to the velocity pointing "in", so I see that eventually this particle reaches a steady state of uniform circular motion (counter clockwise) with radius r = mv/qB

After this point, the field starts to vary in time at, say, dB/dt = c = const >0

I am unsure as to what exactly happens to the particle... here's what I think:

If my expression for the radius is correct, then the particle will eventually (in the limit) come to a rest, since B going up implies r going down.

What I'm particularly confused about is whether or not there is an induced emf in the mean time, due to the circle swept out by the particle... and if so, would it be correct to say that the magnitude of this emf is decaying in time as B goes up? I think this because the flux area is going to zero...

Similarly, if the variation is dB/dt=-c=const<0 then the radius grows... and so does the emf? Albeit flowing the opposite direction to the first case...

This seems weird and, while the math seems straightforward, I'm not so sure about the physics...

Thanks for any explanations!

2. Oct 15, 2012

### cfitzU2

Does no response mean this is really easy or no one knows it?

Because I haven't been able to find a similar issue... :(