Effect on electron in magnetic field

[xiangyu7]

Here's a question that I'm quite confused about:

A uniform constant magnetic field is directed into the page. An electron of constant mass and charge follows a clockwise spiral of decreasing radius path. Is the particle spead increasing or slowing down? and Why?

 

[curly_ebhc]

try this

I see two forces here (sort of, one is a consequense of the other):

1st force (the real one): The electromagnetic force
Look at what you have:
B-field, velocity, charge (its an electron)

2nd force (implied in the motion): Centripital Force
What the first force is doing. Set the two equal. See what happens when you vary radius.

Don't forget Centripital force= mass x centripital acceleration



That should get you through the problem.

curly

 

[quicknote]

The particle's speed is actually increasing in this scenario. This can be explained by the Lorentz force, which states that a charged particle moving in a magnetic field will experience a force perpendicular to both its velocity and the magnetic field. In this case, the electron's velocity is constantly changing as it follows a spiral path, and the force from the magnetic field is always directed towards the center of the spiral. This means that the force is always acting in the direction of the electron's motion, causing it to accelerate and increase its speed.