An oceanographer is studying how the ion concentration in sea water depends on depth. She does this by lowering into the water a pair of concentric metallic cylinders figure 4 at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ?? , outer radius ?? , and length ?. The scientist applies a potential difference ? between the inner and outer surfaces, producing an outward radial current ?. Let ? represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of ?,?,?? , and ??. (b) Express the resistivity of the water in terms of the measured quantities ?,?? ,?? ,?, and ?

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