# Flux through the loop

1. Dec 19, 2005

### 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

2. Dec 19, 2005

### dicerandom

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

3. Dec 20, 2005

### stevo13

Open the attachment for the diagram.

#### Attached Files:

• ###### fluxloop.doc
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4. Dec 21, 2005

### mukundpa

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

5. Dec 22, 2005

### 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.

6. Dec 22, 2005

### mukundpa

whether this flux passes through the hoops or not?

if no no flux through the hoops.

if yes what is its value?

7. Dec 23, 2005

### 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.

8. Dec 24, 2005

### 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

Last edited: Dec 24, 2005
9. Dec 24, 2005

### 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