Calculating Magnetic Field and Induced EMF in a Concentric Loop System

[thebert010]

Homework Statement

A small circular loop of area 2.00 cm^2 is placed in the plane of, and concentric with, a large circular loop of radius 1.00 m. The current in the large loop is changed at a constant rate from 165 A to -165 A (a change in direction) in 1 s, beginning at t = 0. What is the magnitude of the magnetic field B at the center of the small loop due to the current in the large loop at
(a) t = 0
(b) t = 0.500 s
(c) t = 1.00 s
Because the inner loop is small, assume B is uniform over its area.
(e) What emf is induced in the small loop at t = 0.500 s?

Homework Equations

B = μ0I/2r ?
EMF = -dFlux/dt

The Attempt at a Solution

I'm not sure how to start because I feel like the magnetic field at the center due to the large loop will still be affected in part by the small loop, so I'm not sure how to incorporate that to get started...any nudges in the right direction would be greatly appreciated!

Thanks

 

[zhermes]

What effect does the larger loop have on the smaller loop?

 

[thebert010]

What effect does the larger loop have on the smaller loop?

I have no idea, i feel like that's what I need to know to start the problem. all i can think is that the magnitude at the center initially is B=(4*pi*e-7 Tm/A)(165 A)/ 2*.01m since the two circles share a common center and there is no initial current running through the smaller loop...I feel like I am making an incorrect assumption though because that seems too easy

 

[zhermes]

But there's going to be a change in flux through the smaller wire right? *hint hint, wink wink*

 

[thebert010]

But there's going to be a change in flux through the smaller wire right? *hint hint, wink wink*

So i figured the flux of the smaller loop (flux = BA) would just be the Magentic Field due to the current from the larger loop * the given area of the small loop. and would change as B changes due to the current changing. Is this the right way to look at it, or am I still on the wrong track? ...sorry, I'm at work and having a rather hard time getting to the internet :(

 

[zhermes]

No worries, and yeah you're totally on the right track. So what effect does that changing magnetic flux have on the wire?

And backing up to parts a,b,c--I think all they want is the 'too simple' answer you gave in the beginning. (You could make a more accurate answer, but I don't think that's what they're looking for).

 

[thebert010]

No worries, and yeah you're totally on the right track. So what effect does that changing magnetic flux have on the wire?

And backing up to parts a,b,c--I think all they want is the 'too simple' answer you gave in the beginning. (You could make a more accurate answer, but I don't think that's what they're looking for).

if I'm not mistaken, i believe the change in magnetic flux will induce a current to run through the wire of the smaller loop of EMF = -dFlux/dt. my only snag at this point is that the magnetic field at t=.5 sec, since the sign of the current is only to distinguish direction, the 165A would be 165/2 A instead of 0 A (which would instead be an avg of 165A and -165A). Sound good?

 

[zhermes]

You're right on the first part, but at t=0.5s, it will be 0--even though the negative sign does me the opposite direction. Think about it this way: if you're on a straight road (can't turn) driving 20 mph, and over the course of 10sec change to going -20mph. You have to 'pass by' going 0 mph somewhere inbetween.

 

[thebert010]

You're right on the first part, but at t=0.5s, it will be 0--even though the negative sign does me the opposite direction. Think about it this way: if you're on a straight road (can't turn) driving 20 mph, and over the course of 10sec change to going -20mph. You have to 'pass by' going 0 mph somewhere inbetween.

AH! who would have thought this would involve a completely rational explanation ;-) ha, thanks so much for all of your help - it's all making damn near perfect sense now!