Question About Induced Currents in Three Different Coils

[Lunar Manatee]

Homework Statement

The question asks for the relation between the induced currents in three different coils M, L and K entering the same magnetic field B. (see pictures attached)

Relevant Equations

I came up with a solution; my teacher said it was wrong and presented me with what seemed to be a wrong answer, I am not sure. What/Who is correct?

I did the work (multiple times, and multiple ways--which are pretty much the same) and came up with: I_K>I_M=I_L (please see pictures attached for question, my solution and teacher's solution-which was I_K>I_L>I_M)

 

[kuruman]

I got the same answers as you. The solution seems to think that the area of the loop is relevant in the calculation. Since the field is uniform and static, the change in magnetic flux is the change in area and that's what counts. $$\frac{d\Phi}{dt}=B\frac{dA}{dt}=By\frac{dx}{dt}=Byv$$ where y is the height of eaach coil, $a$, $a$ or $2a$. The factor $a^2$ should never be part of the picture.

Whoever wrote this "solution" seems to think that $\dfrac{d\Phi}{dt}$ is the same as $\dfrac{\Phi}{t}$. It is not.

 

[Lunar Manatee]

I got the same answers as you. The solution seems to think that the area of the loop is relevant in the calculation. Since the field is uniform and static, the change in magnetic flux is the change in area and that's what counts. $$\frac{d\Phi}{dt}=B\frac{dA}{dt}=By\frac{dx}{dt}=Byv$$ where y is the height of eaach coil, $a$, $a$ or $2a$. The factor $a^2$ should never be part of the picture.

Whoever wrote this "solution" seems to think that $\dfrac{d\Phi}{dt}$ is the same as $\dfrac{\Phi}{t}$. It is not.

Thanks so very much, I knew my answer was correct but I needed the extra confirmation.

Yeah, the teacher ended up making me have to try to prove it to them with calculus; they still disagreed.

Glad you answered so quickly, much appreciated.

 

[hutchphd]

I am confused as to the assumptions made about resistance of the wires. Presumably R will be proportional to the perimeter of each figure. Am I missing something?

 

[Lunar Manatee]

I am confused as to the assumptions made about resistance of the wires. Presumably R will be proportional to the perimeter of each figure. Am I missing something?

It's an oversimplified question, but the coil's wire itself is of neglegible resistance (or zero in this case), the coils' resistances (which you can think of as an actual device/resistor connected in series) are listed just after the question and before the drawing, suppose that R_M=R and work from there.

Sorry for the confusion!

 

[hutchphd]

Then the question makes no sense. The sizes of the currents will depend critically upon R. Vanishingly amall R will lead to infinite currents. I would like to see the complete concise problem statement....
EDIT Oh I see the parenthetical resistances. This is then a very bad badly conceived problem which misses most of the physics. I dislike it intensely.

 

[Lunar Manatee]

Then the question makes no sense. The sizes of the currents will depend critically upon R. Vanishingly amall R will lead to infinite currents. I would like to see the complete concise problem statement....
EDIT Oh I see the parenthetical resistances. This is then a very bad badly conceived problem which misses most of the physics. I dislike it intensely.

I copied it word for word (I think. I did rewrite it in LaTeX at 3 AM out of pure frustration with the solution tbh, hah)

 

[kuruman]

I am confused as to the assumptions made about resistance of the wires. Presumably R will be proportional to the perimeter of each figure. Am I missing something?

Nobody mentioned that the wires forming the loops have the same diameter and resistivity. What matters is the given resistance of each. The biggest worry here is with the solution that is clearly wrong.

Yeah, the teacher ended up making me have to try to prove it to them with calculus; they still disagreed.

Can you change teachers? Probably not, but rest assured that we will be here to help you if you have more questions of this sort in the future.

 

[hutchphd]

Nobody mentioned that the wires forming the loops have the same diameter and resistivity. What matters is the given resistance of each. The biggest worry here is with the solution that is clearly wrong.

Yes wrong is worse than completely arbitrary. I think a different teacher would be an excellent solution if possible

 

[PhDeezNutz]

I’m getting the same answer as the OP. I also want to take a second to admire the time taken to draw the figure in Latex.

 

[Lunar Manatee]

I’m getting the same answer as the OP. I also want to take a second to admire the time taken to draw the figure in Latex.

That's a good sign! Thanks for the confirmation!

Appreciate your admiration of the LaTeX thingie I made, I tried haha.