Is the Magnetic Field Strength Increasing or Decreasing?

[Jus10]

So the main reason I'm posting about this problem is that one of the teaching assistants helped me with this problem, but a buddy of mine got something different on part A and part B (Assess). So I wanted to post up here and see what you guys say.

1. Homework Statement

The loop in the figure has an induced current as shown. The loop as a resistance of 0.10Ω.

Part A) Is the magnetic field strength increasing or decreasing? Explain how you determined your answer.

Part B) What is the rate of change of the field ΔB/Δt?
(Prepare)
(Solve)
(Asses) How would your answers change if the drawn current direction were reversed?

Homework Equations

ε=IR
ε=(ΔB/Δt)A

The Attempt at a Solution

Part A) The applied field is decreasing because the flux is out of the page & the current is counter-clockwise.

Part B) (Prepare) I = 0.15 A
R = 0.10 Ω
A = 6.4e^-3

(Solve) ε = (0.15)(0.10)
ε = 0.015 V

0.015 = (ΔB/Δt)(6.4e^-3)
ΔB/Δt = 0.015/6.4e^-3
ΔB/Δt = 2.34 T/s

(Assess) If the current were reversed, the applied field would be INCREASING. So, instead of DECREASING by 2.34 T/s, it would INCREASE by 2.34 T/s

 

[andrewkirk]

It looks right to me (provided your interpretation of the meaning of the Xs is correct - see TSny's post below).

 

[TSny]

The Attempt at a Solution

Part A) The applied field is decreasing because the flux is out of the page & the current is counter-clockwise.

Don't the X's in the picture denote "into the page" rather than "out of the page"?

For part (b) did you express the answer in the correct units?

 

[Jus10]

Don't the X's in the picture denote "into the page" rather than "out of the page"?

For part (b) did you express the answer in the correct units?

Yes, the X's denote into the page. Dots denote out of the page. I originally had it opposite to what I've posted here, but the TA said it was wrong. So I changed it to the above, and she approved. It's a bit confusing now, but i figured the into the page meant the field was decreasing, but per the right hand rule, the current would be in the opposite direction (clockwise instead of counter-clockwise).

I meant Teslas, not Joules. Good catch. I don't know why I put Joules.

 

[TSny]

Yes, the X's denote into the page. Dots denote out of the page.

OK, the B field shown in the picture is into the page.

I originally had it opposite to what I've posted here, but the TA said it was wrong. So I changed it to the above, and she approved. It's a bit confusing now, but i figured the into the page meant the field was decreasing, but per the right hand rule, the current would be in the opposite direction (clockwise instead of counter-clockwise).

I think the TA is mistaken here. As you say, if the B field is decreasing, then the induced current would be clockwise. So, the B field must be increasing.

 

[Jus10]

OK, the B field shown in the picture is into the page.

I think the TA is mistaken here. As you say, if the B field is decreasing, then the induced current would be clockwise. So, the B field must be increasing.

Ok. That's what I originally thought. Now I know why I'm having such a hard time in this class, because one person says one thing and another says another, and it just really confuses me. I'm going to start going to another TA for guidance.

I'm also questioning my other problems now. If it's ok, I'm going to start other threads with the other problems and what I've got and so we can make sure I'm doing this right. I really appreciate everyone's help with this.

Just to verify, this is what I modified my answers to:
Part A) The applied field is increasing because the flux is out of the page and the current is counterclockwise , per the right hand rule.

Part B) If the current were reversed, the applied field would be decreasing. Instead of increasing by 2.34 T/s, it would decrease by 2.34 T/s

 

[TSny]

Part A) The applied field is increasing because the flux is out of the page and the current is counterclockwise , per the right hand rule.

The applied field is increasing because the flux of the applied field is into the page and the induced current is counterclockwise. (The flux inside the square produced by the induced current will be out of the page.)

Can you give a detailed explanation of the answer to the problem as you see it so that we can make sure your reasoning is correct? Your answer should include using the right hand rule as well as using Lenz's law.

Part B) If the current were reversed, the applied field would be decreasing. Instead of increasing by 2.34 T/s, it would decrease by 2.34 T/s

Yes.

 

[Jus10]

Can you give a detailed explanation of the answer to the problem as you see it so that we can make sure your reasoning is correct? Your answer should include using the right hand rule as well as using Lenz's law.

So, Lenz's Law states the direction of the induced current is such that the induced magnetic field opposes the change in the flux (from my book). Because the changing flux is into the page, the current is counter-clockwise, opposing the changing flux. The right hand rule, curling the fingers in the direction of the current, shows the applied field to be out of the page due to the direction the thumb is pointing.

 

[TSny]

So, Lenz's Law states the direction of the induced current is such that the induced magnetic field opposes the change in the flux (from my book). Because the changing flux is into the page, the current is counter-clockwise, opposing the changing flux. The right hand rule, curling the fingers in the direction of the current, shows the applied field to be out of the page due to the direction the thumb is pointing.

OK. That sounds good!

And when you say "the changing flux is into the page", that's the same as saying the applied field is increasing in this case.

 

[Jus10]

Awesome! I think I'm really starting to understand this. Just one more question just to fully nail this into my knowledge bank. An induced field is just a magnetic field, and an applied field is the electromagnetic field that is generated with a changing induced field?

 

[TSny]

The applied field is the magnetic field represented by the X's in the picture. It is best described as a magnetic field rather than an electromagnetic field. This field is being produced by some source not shown in the figure. The source could be a magnet or a current in some other circuit.

The induced field is the magnetic field produced by the induced current. As you said, this induced field creates a flux through the square that is out of the page and therefore opposes the increasing flux into the page due to the increasing strength of the applied magnetic field.

 

[Jus10]

The applied field is the magnetic field represented by the X's in the picture. It is best described as a magnetic field rather than an electromagnetic field. This field is being produced by some source not shown in the figure. The source could be a magnet or a current in some other circuit.

The induced field is the magnetic field produced by the induced current. As you said, this induced field creates a flux through the square that is out of the page and therefore opposes the increasing flux into the page due to the increasing strength of the applied magnetic field.

Awesome! I think I got it now. I really appreciate you taking the time to hash through the details of this problem with me!