(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a conductor with the square-shaped area. the Radii are r_{1}, r_{2 }with width b and resistivity ## \rho_R##.

Find the resistance R between A and B

2. Relevant equations

##I = \iint_A\vec J \cdot d \vec A##

## \vec J = \kappa \vec E ##

## \vec E = \rho \vec J##

## V = \int\vec E\cdot d\vec s ##

## V = IR##

3. The attempt at a solution

## I = \iint_A\vec J \cdot d \vec A = Jb(r_2-r_1)##

## \vec J = {\frac{I}{b(r_2-r_1)}}\hat e_\theta ##

## \vec E = \rho_R \vec J = (\rho_R I/b(r_2-r_1) ) \hat e_\theta##

## V = \int_0^\pi \vec E\cdot d\vec s ##

## d \vec s = r d\theta \hat e_\theta ##

## V = {\frac{\pi \rho_R I r}{b(r_2-r_1)}}##

The Total Voltage

## \int d V = \int {\frac{\pi \rho_R I d r}{b(r_2-r_1)}} ##

After integration over ##[r_1, r_2]##

## V = IR = {\frac{\pi \rho_R I}{b}} ##

## R = {\frac{\pi \rho_R }{b}} ##

I don't know, if the solution is right. It is a bit weird since R is not dependent of the Radii but the units are right.

I hope someone can clear my confusion and help me :)

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# Homework Help: Resistance of a semicircular conductor with a rectangular cross section

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