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**1. Homework Statement**

The question gives a coil of N turns carrying a current of I Amperes wound on a ring with rectangular cross section of inner radius r1 and outer radius r2 and height h. The ring has magnetic permeability mu. What is the flux in webbers?

**2. Homework Equations**

Ampere's Law:

Closed Integral (B * ds) = mu * I

**3. The Attempt at a Solution**

My problem is mostly a conceptual one since I have all the equations for sure.

flux = closed integral (B * dA)

integral (B * ds) = B integral (ds) = B (2 pi r) = mu * N * I

since it has N loops

B is not constant, so for flux we must integrate:

flux = integral (B dA) = integral (mu*N*I/(2 pi r) dA)

This is where I'm confused:

the solution says:

"The area element dA can be expressed as dA = h dr where h is the height of the rectangular cross section."

Then it proceeds to integrate from r1 to r2 to get: flux = N*I*h/(2 pi)*mu*ln(r2/r1) and the question is solved. But I don't understand how that substitution can be made. Doesn't that imply dA/dr = h so A is a function of r, or A = hr + c??

Any help will be appreciated greatly.

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