What Is the Flux Through a Disk-Shaped Area in a Solenoid?

[flyingpig]

Homework Statement

Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is
positioned perpendicular to and centered on the axis of the solenoid as shown below

The Attempt at a Solution

$$\oint \vec{B} \cdot \vec{dA} = \Phi_{B}$$

$$\vec{B} = \frac{\mu_0 I N}{l}$$

$$\vec{B} \cdot (\pi R^2 l) = \Phi_{B}$$

$$2\mu_0 \pi INR^2 = 7.106 \times 10^{-5}Wb$$

My book has 7.40uWb.

For my "surface area", I had $$\pi r^2$$ for the circle and I times it by l because that's how long the cylinder is. I know that is volume but I already tried other possible "areas" like just πr² and 2πrl

 

[ideasrule]

I think you forgot to attach the diagram. Based on your description alone, I think your solution is correct, except that area should be pi*r^2 instead of pi*r^2*l. (I know you already tried that, but unless the diagram shows something I haven't considered, it should definitely be correct.)

 

[flyingpig]

I think you forgot to attach the diagram. Based on your description alone, I think your solution is correct, except that area should be pi*r^2 instead of pi*r^2*l. (I know you already tried that, but unless the diagram shows something I haven't considered, it should definitely be correct.)

My idiocy is truly unparalleled

http://img857.imageshack.us/i/78891006.png/

Uploaded with ImageShack.us

 

[ideasrule]

The figure does indeed show something I haven't considered. B is 0 outside of the solenoid, so the effective area you should use in calculating the flux should be the cross-sectional area of the solenoid. Are you given that value?

 

[flyingpig]

Yeah just let me wash my hands first because I was eating and writing at the same time and I just spilled my drink...

 

[flyingpig]

Yup, the radius of the solenoid is r = 1.25cm. The length of the of the solenoid is 30.0cm, the current through it is 12A and there are 300 turns

 

[ideasrule]

So have you tried using pi*r^2 as your area, with r=1.25 cm?

 

[flyingpig]

Yes I got the answer I forgot to note that lol sorry