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 (Fig. P27.68) 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 ra, outer radius rb , and length L much larger than rb. The scientist applies a potential difference ?V between the inner and outer surfaces, producing an outward radial current I. Let ρ represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, ρ, ra, and rb. (b) Express the resistivity of the water in terms of the measured quantities L, ra, rb , ?V, and I.

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 (Fig. P27.68) 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 ra, outer radius rb , and length L much larger than rb. The scientist applies a potential difference ?V between the inner and outer surfaces, producing an outward radial current I. Let ρ represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, ρ, ra, and rb. (b) Express the resistivity of the water in terms of the measured quantities L, ra, rb , ?V, and I.