Compute flux through rectangular area

[EV33]

Homework Statement

There is an aXb rectangular area in the same plane as a wire with current I. The wire is parallel to side b, and a distance d away. Compute the flux through the rectangular area.

Homework Equations

$$\Phi$$=$$\int$$B*dA

B=($$\mu$$I)/(2$$\pi$$r)

cylindrical coordinates... rdrd$$\theta$$dz

The Attempt at a Solution

($$\mu$$I)/(2$$\pi)$$$$\int$$$$\int$$$$\int$$(1/r)(rdrd$$\theta$$dz)

dr is from d to d+a
d$$\theta$$ is from 0 to 2$$\pi$$
dz is from 0 to b

The solution to this ends up having natural logs in it, and to do that I would have to drop r, but I don't feel like that is right. Could someone please help point me in the right direction on setting up this integral.

Thank you.

 

[EV33]

I am not sure why some things look like subscripts or exponents so just a warning there are no exponents are subscripts lol

 

[EV33]

I think I see why now. I should be using rectangular coordinates huh?
I don't know what I was thinking... I must have been thinking partially of amperes law

 

[EV33]

($$\mu$$I)/(2$$\pi)$$$$\int$$$$\int$$(1/r) dr dy

dr from d to d+a
dy from 0 to b

would this be the correct set up?

 

[ideasrule]

Yes, that's the correct setup. Your solution should have a natural log in it.

 

[Gregg]

($$\mu$$I)/(2$$\pi)$$$$\int$$$$\int$$(1/r) dr dy

dr from d to d+a
dy from 0 to b

would this be the correct set up?

$$\frac{ \mu I }{2\pi} \int_0^b \int_d^{d+a} \frac{1}{r} dr dy$$

\frac{ \mu I }{2\pi} \int_0^b \int_d^{d+a} \frac{1}{r} dr dy

Hope that helps, though it's nothing to do with the actual question.