More Magnetic Fields -- 2 fields through a loop decreasing with time....

[Jus10]

This is a continuation of a previous thread in which I was informed my TA was mistaken on an aspect of magnetism. This thread is just to verify another problem within the homework is correct. Other threads will be posted to continue.

1. Homework Statement

A) What is the magnetic flux through the loop shown in the figure.

B) If both magnetic fields begin to decrease in magnitude, what is the direction of the induced current in the loop? Explain with Lenz's Law.

Homework Equations

Φ = BA

The Attempt at a Solution

Part A) Φ = (B_inA_in)-(B_outA_out)
Φ = (2.0)(0.2²)-(1.0)(0.2²)
Φ = 0.04 Wb

Part B) The induced field would act in the direction of the applied field if B is decreasing. Therefore, the current would be flowing clockwise.

 

[BiGyElLoWhAt]

The only thing I would point out, is for part B), $V=\frac{d\Phi}{dt} = \frac{d(\vec{B}_{left}\cdot \vec{A}_{left}+\vec{B}_{right}\cdot\vec{A}_{right})}{dt}$
You seem to be implicitly assuming that they are both decreasing at the same rate. It's the rate of change that gives you the induced voltage, and thus the corresponding current. Unless it says that they are both increasing or decreasing at a given (possibly relative) rate, then this problem is unsolveable.

 

[BiGyElLoWhAt]

Perhaps it says that in the picture. On the LHS-bottom, it appears to say something about magnitude.

 

[Jus10]

The only thing I would point out, is for part B), $V=\frac{d\Phi}{dt} = \frac{d(\vec{B}_{left}\cdot \vec{A}_{left}+\vec{B}_{right}\cdot\vec{A}_{right})}{dt}$
You seem to be implicitly assuming that they are both decreasing at the same rate. It's the rate of change that gives you the induced voltage, and thus the corresponding current. Unless it says that they are both increasing or decreasing at a given (possibly relative) rate, then this problem is unsolveable.

Perhaps it says that in the picture. On the LHS-bottom, it appears to say something about magnitude.

It doesn't specify the rate of decrease. It just states, "If bothmagnetic fields begin to decrease in magnitude, what is the direction of the induced current in the loop? Explain with Lenz's Law." The phrase at the LHS-bottom of the image is just Part B.

 

[BiGyElLoWhAt]

Well, you can't answer this question, then (at least without an assumption). You're probably supposed to assume that they are decreasing at the same rate. You'll need a better explanation than what you have (You haven't even mentioned Lenz's law), but other than that and stating, clearly, your assumption, I would say what you have is correct.