Correct statement about coils moving in and out of a magnetic field

[songoku]

Homework Statement

Please see "attempt at a solution"

Relevant Equations

Fleming left hand rule
Fleming right hand rule
Faraday's law
Lenz's law
F = BIL sin θ

Option B is correct. Using Lenz's law, the direction of current flowing in coil 1 is counter clockwise while in coil 2 is clockwise.

Option A is correct. Using Fleming's left hand rule, the resultant magnetic force acting on the both coils is to the left.

I am not sure about option C and D. I think the answer is D because coil 2 is moving out of the magnetic field so variable L of the formula F = BIL sin θ decreases therefore to maintain constant speed it has to maintain constant value of F by increasing the induced current. Am I correct?

Thanks

 

[mfb]

Your answer is correct but for the wrong reasons. Your formula only applies to coils rotating in a homogeneous magnetic field.
The induction is proportional to the change in flux through the coils. Apart from the velocity and the magnetic field strength inside the field (both are constant), what changes? What is a geometrical property that is proportional to this change? Is it increasing or decreasing for coil 1 and 2?

 

[songoku]

Your answer is correct but for the wrong reasons. Your formula only applies to coils rotating in a homogeneous magnetic field.
The induction is proportional to the change in flux through the coils. Apart from the velocity and the magnetic field strength inside the field (both are constant), what changes? What is a geometrical property that is proportional to this change? Is it increasing or decreasing for coil 1 and 2?

Current is induced in both coils because there's is change in magnetic flux caused by change in area of coil inside the magnetic field. Area of coil 2 decreases while area of coil 1 increases but induced current is proportional to the rate of change of the area and I am not sure how to determine the rate of change of area.

 

[rude man]

Current is induced in both coils because there's is change in magnetic flux caused by change in area of coil inside the magnetic field. Area of coil 2 decreases while area of coil 1 increases but induced current is proportional to the rate of change of the area and I am not sure how to determine the rate of change of area.

Move each coil a small displacemen in the picture, stop & look at the respective areas of the slivers left behind. Which is the bigger area?

 

[songoku]

Move each coil a small displacemen in the picture, stop & look at the respective areas of the slivers left behind. Which is the bigger area?

I see. I think the rate of change of area of coil 2 will increase at first then decrease so the magnitude of induced current will also undergo same change (increase then decrease), while rate of change of area 1 decreases means that option C is correct.

Am I correct? Thanks

 

[mfb]

Right.
The magnitude of the change is linked to the height of the coil at the edge of the magnetic field.

 

[songoku]

I have one more question

Your formula only applies to coils rotating in a homogeneous magnetic field.

I never know F = BIL sin θ is for rotating coil. I thought it is for current - carrying wire put in magnetic field and θ is angle between B and direction of current. Should the wire rotate to experience magnetic force?

 

[mfb]

Ah, I misinterpreted your equation. Well, the concept is very similar.

 

[songoku]

Thank you very much for the help mfb and rude man

 

[Delta2]

I also agree that options A-C are correct, hence leaving option D as the only false option but I got one question:

How you were able to determine that the rate of change of surface for coil 1 is a decreasing function without going into detailed calculations (expressing the area as a function of the distance that the coil is inside the B-field area and then taking the derivative of that assuming that distance is a function of $ct$ where c the constant velocity with which each coil is moving)?

 

[rude man]

I have one more question
I never know F = BIL sin θ is for rotating coil. I thought it is for current - carrying wire put in magnetic field and θ is angle between B and direction of current. Should the wire rotate to experience magnetic force?

If there is current in the coil the answer is no. Your formula F = BIL sin θ applies.
But if you want to generate a current in the coil then it would have to move (emf = -d$\phi$/dt with $\phi$ changing with time by virtue of the rotating coil.

The two concepts are basically different. F = BIL sin θ is based on the Lorentz magnetic force on moving charge whereas the emf formula above rests on one of Maxwell's equations as first formulated by Faraday.

 

[songoku]

I also agree that options A-C are correct, hence leaving option D as the only false option but I got one question:

How you were able to determine that the rate of change of surface for coil 1 is a decreasing function without going into detailed calculations (expressing the area as a function of the distance that the coil is inside the B-field area and then taking the derivative of that assuming that distance is a function of $ct$ where c the constant velocity with which each coil is moving)?

Bu using help in post #4. Draw the area entering the magnetic field every 1 mm and I see the area entering the magnetic field is decreasing

If there is current in the coil the answer is no. Your formula F = BIL sin θ applies.
But if you want to generate a current in the coil then it would have to move (emf = -d$\phi$/dt with $\phi$ changing with time by virtue of the rotating coil.

The two concepts are basically different. F = BIL sin θ is based on the Lorentz magnetic force on moving charge whereas the emf formula above rests on one of Maxwell's equations as first formulated by Faraday.

Haven't learned about Maxwell's equation but I think I get the general idea

 

[rude man]

Bu using help in post #4. Draw the area entering the magnetic field every 1 mm and I see the area entering the magnetic field is decreasing

Haven't learned about Maxwell's equation but I think I get the general idea

You'll get Faraday's law first, if you haven't already.
The Maxwell equations include Faraday but also extend relationships between E and B fields and form the basis of electromagnegic waves. They are truly marvelous; I hope you encounter them.