Potential difference and resistance. A conducting sphere of radius a, with conductivity u is cut into two hemispheres. Then, each hemisphere is trimmed so that it has a flat surface on top and the two sections are connected as shown in Figure 7.35. A uniform current density J crosses the upper flat surface as shown.

(a) Calculate the potential difference between A and B.

(b) Compare the result in (a) with that obtained in problem 7.14a.

Problem 7.14

Calculation of resistance. A sphere made of a conducting material with conductivity 0" is connected in a circuit as shown in Figure 7.35a. For connection purposes, the sphere is trimmed and connections made to the flat surfaces created by the cuts. The resistance R and source voltage V are known.

(a) Calculate the potential on the sphere (between points A and B) in terms of the known parameters.