8/05 Because we were short of time, I did not give you today's ungraded HW during lecture. Here it is: Consider a series AC circuit with a generator, a resistor, and a capacitor, and with inductance which is small enough to ignore. R = 45 kOhms, C = 355 pF, and the driving angular frequency is 100,000 rad/s. The capacitor voltage has been measured to be (0.262 V) times a sine function of omega_driving times the time. Show that the maximum resistor voltage must be 0.419 V, and that the maximum generator EMF must be 0.494 V. 7/23 Because we were short of time, I did not give you today's ungraded HW during lecture. Here it is: Show how to use the Biot-Savart Law to show that (a) For a current segment of length L oriented on the y axis from the origin to the point (0,L), with the current in the +y direction, the magnetic field strength created at a point P at location x on the x axis is B = (k/c^2)*(IL/(x*sqrt(L^2+x^2))). (b) For a quarter circle (radius R) of current I flowing clockwise from the point (-R,0) to the point (0,R), the magnetic field strength created at the origin is B = mu_0*I/(8*R). Thanks. GBA 7/17 Because we were short of time, I did not give you today's ungraded HW during lecture. Here it is: A metal rod sticking vertically into the ground has just been struck by lightning. As a result, a momentary current of size I is flowing from the bottom of the rod into the ground; assume that this current is spreading uniformly into a hemisphere of ground centered at the bottom end of the metal rod. At this location, the resistivity of the ground has a value rho. Show that, while the current I is flowing, there must be an electric field of magnitude E(r) = rho*I/(2*pi*r^2) existing within the ground near the bottom end of the metal pole, where r represents the distance from the bottom end of the pole. Thanks. GBA 7/15 I neglected to give you the ungraded HW for today. Here it is. Use Gauss' Law and the definition of capacitance to show that nested, concentric, spherical metal shells of radius a and b (b>a) have a capacitance of (k*((1/a)-(1/b)))^(-1). 6/26 No Updates Yet