Re: [Phys-L] charge in an increasing magnetic field

["Trivilino, Herman" <HTrivilino@com.edu>]

I agree that there is no way to define the center of a uniform field. Therefore the problem can be restated as a charged particle at rest in a uniform magnetic field, pointing in the z-direction and increasing linearly with time. I also agree that if you had a loop of wire, forming a circle that lies in the xy-plane for example, there would be an induced EMF causing current to flow in that loop. So, on each of the charge carriers in the loop there is an electric force, and thus there must be an electric field that's the source of that electric force.
 
> From there you can analyze the situation as you did with r equaling the radius of the circular loop. I'm by no means fluent in Maxwell's equations and I'm in awe of those who are, but intuition tells me that you need a distribution of charge to get the induced EMF described by Faraday's Law.
 
Herman Trivilino
Physics Professor
Professional Development Academy Leader
College of the Mainland
www.com.edu <http://www.com.edu/> 
 

________________________________

From: Phys-l on behalf of Philip Keller
Sent: Wed 15-Apr-15 11:23 AM
To: Phys-L@phys-l.org
Subject: [Phys-L] charge in an increasing magnetic field



Hello all,

I know I have asked variations of this question in the past, but I am still
working on this one...

A region of space is filled with a uniform magnetic field, directed in the
z-direction, increasing linearly with time, with the "center of the field
at the origin.  A small positively charged object located at the point (1
m, 0, 0) is released from rest.

I am trying to understand the resulting motion of the particle.  Is any of
what I have so far correct:

At any point, it experiences a force caused by the induced electric field
associated with the changing magnetic field.  That force is tangential to
the circle of radius r, where r represents the distance from the current
position to the center of the field.  I think I can show that the field =
r/2 times dB/dt. That force increases the speed of the particle.

At any point, it also experiences the magnetic force that acts on any
particle moving perpendicularly through a magnetic field.  But this field
happens to be increasing.  This force changes the direction of the
particle's motion.

I am having trouble visualizing the resulting motion that these two forces
lead to..  Can anyone point me to a discussion of this topic?  I am also
going to try to model this in interactive physics to see if I can get a
hint that way.  Also, are there practical applications?

Thanks
Phil
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