Monday homework problem 11.9 the circular solenoid drawn to the right has a radius r. a square loop of wire with 1 turn and normal parallel to the axis of the solenoid is inside the solenoid. the length of one side of the square loop is ℓ. the solenoid is wound with n turns of over a length d. the current through the solenoid is i(t) = γt2 where γ is a constant. the system is drawn to the right. the magnetic field in the solenoid points out of the page as drawn. calculate the emf around the square loop (dark square) as a function of time.

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.