Flux through the loop

[stevo13]

Here is the problem: You have a loop of radius r1 and r2. You have a rectangle with dimensions of length a and b (b>a) with a uniform magnetic field only passing through this rectangle, into the page. What is the magnetic flux through the loop? To better help visualize the diagram, the length b is parallel to the y-axis, while the length a is parallel to the x-axis. This problem was on our final (I'm taking the calculus based physics course). If someone could work this out so I could compare it with what I did at home (assuming I did it the same as on the final) I would appreciate it. Thanks.

Steve

[dicerandom]

Could you include a diagram? I assume the loop is smaller than the rectangle?

[stevo13]

Open the attachment for the diagram.

[mukundpa]

What is your work

Is there is any flux passing through the loops, other then the flux through the rectangle.

[stevo13]

The only location the magnetic field passes through is the through the rectangle. Since there isn't a uniform magnetic field passing through the hoop, you have to use the definition flux=int B dA.

[mukundpa]

whether this flux passes through the hoops or not?

if no no flux through the hoops.

if yes what is its value?

[stevo13]

The magnetic field is B. There is no numerical value. The rectangle is circumscribed within the solid loop of radius R1 and R2, therefore, the magnetic field also passes through the loop; but only through the rectangle...nowhere else. I will tell you this, the two radii confused me at first. I would think that if we were dealing with a loop the radius would be just R. On the other hand, if the shape was described as a ring then the two different radii would make sense. Hope this helps.

[mukundpa]

The dog beautifully passed through the fire ring!!

In any of the case, if we have two circular rings of radii r_1 and r_2 ,or a circular thin strip of inner radius r_1 and thickness r_2 - r_1
the flux of magnetic field B is passing through it, but only within the area A and hence \phi = B.A = Bba.

MP

[mukundpa]

In the circus the dog beautifully passed through the fire ring!!

In any of the case, if we have two circular rings of radii r_1 and r_2 ,or a circular thin strip of inner radius r_1 and thickness r_2 - r_1
the flux of magnetic field B is passing through it, but only within the area A and hence \phi = B.A = Bba.


MP