Hi all,

I am a 2nd semester general physics student and have a problem I'm
trying to figure out. Here is the problem and my attempt.

A uniform magnetic field is established perpendicular to the plane of a loop
of radius 5.0 cm, resistance .4 ohm and negligible self-inductance. The
magnitude is increasing at a rate of 40mT/s. Find the rate of Joule heating
in the loop.

My attempted work

F=NBA
dF/dt=NA(dB/dt)

N=1
A=3.14*.05^2=.00785 m^2
dB/dt=40*10^6

dF/dt=314,000 T m^2/s

This is all I've done so far, and I don't think it's even right to start
out. I think that this is probably a classic Related Rates problem from
differential calculus, but am unsure how to go about it. Any help would be
appreciated.

Thanks!
David Moran

In article ,
David Moran wrote:

A uniform magnetic field is established perpendicular to the plane of a loop
of radius 5.0 cm, resistance .4 ohm and negligible self-inductance. The
magnitude is increasing at a rate of 40mT/s. Find the rate of Joule heating
in the loop.

My attempted work

F=NBA
dF/dt=NA(dB/dt)

N=1
A=3.14*.05^2=.00785 m^2
dB/dt=40*10^6

dF/dt=314,000 T m^2/s

This is all I've done so far, and I don't think it's even right to start
out.

No, it looks like you're OK so far, assuming that "mT" means microtesla
and F is the magnetic flux.

By Faraday's Law, dF/dt equals the magnitude of the electromotive force
around the loop (in volts, since you're using MKSA units). Now, if you
have a loop of wire with s specified emf (which could just as well come
from a battery) and a specified resistance, what is the current in the
loop? And what is the power dissipated by that current, passing through
that resistance?

--
Jon Bell Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA