With the question
An oceanographer is studying how the ion concentration in seawaterdepends on depth. She makes a measurement by lowering into thewater a pair of concentric metallic cylinders at the end of a cableand taking data to determine the resistance between theseelectrodes as a function of depth. The water between the twocylinders forms a cylindrical shell of inner radius ra, outerradius rb, and length L much larger than rb. The scientist appliesa potential difference ?V between the inner and outer surfaces,producing an outward radial current I. Let ? represent theresistivity of the water.
We realize that we integrate resistivity(Length/area) but then fromthe solution shown we integrate dR= resistivity(dr/(2pirL)) Weunderstand everything but why the L goes to the bottom of thisintegration.
Thanks.
With the question
An oceanographer is studying how the ion concentration in seawaterdepends on depth. She makes a measurement by lowering into thewater a pair of concentric metallic cylinders at the end of a cableand taking data to determine the resistance between theseelectrodes as a function of depth. The water between the twocylinders forms a cylindrical shell of inner radius ra, outerradius rb, and length L much larger than rb. The scientist appliesa potential difference ?V between the inner and outer surfaces,producing an outward radial current I. Let ? represent theresistivity of the water.
We realize that we integrate resistivity(Length/area) but then fromthe solution shown we integrate dR= resistivity(dr/(2pirL)) Weunderstand everything but why the L goes to the bottom of thisintegration.
Thanks.
