- #1
Basel H
- 2
- 0
Homework Statement
There is a conductor with the square-shaped area. the Radii are r1 , r2 with width b and resistivity ## \rho_R##.
Find the resistance R between A and B
2. Homework 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##
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)}} ##[/B]
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 :)