2. Explain the meaning of each term in the following equation: V . (a.VT) - plyup . VT + GE . ET = AT (PC;T) (1) 3. Determine the voltage distribution as a function of radius away from an infinitely long cylindrical electrode V(r). For this problem assume that the voltage at the radius of the electrode ry is Ve and the voltage at r, is Vo. Hint, solve the equation V V = 0 in the radial co-ordinate system. 4. Now that you have an equation for the voltage distribution, determine the electric field as a function of r E(r). Recall that E = V . V. We use the electric field to determine the power density distribution as in Equation 1 (GE . E). 5. Assume that the conductivity of the soil is 0.05 5/m, V. is 200 V, and Vo is zero. Plot the voltage, electric field, and power density as a function of r for Or, S r. What can you say about the results?6. Now that you know the power density at the surface of the electrode, determine how long it takes for the temperature there to go from 20"C to 100"C. Use the physical properties used elsewhere in the exam or make assumptions as needed. Don't be surprised by the answer. 7. Using the equation for the power density in the previous question, plot the temperature distribution as a function of radius. The relevant equation to solve is Equation 2 GE . ET = = (PG.T) (2) 8. Bonus Question. If you answer this question correctly, provide the solution and a graphical output of your solution your bonus will be 100 dollars. Solve the following Equation 3 (this is Equation 1 assuming no heat transfer by thermal conduction is negligible). Notice that the minus sign indicates that we are injecting water into the electrode. -plyup . VT + of . ET = - (PG.T) (3)