PROBLEM 3 In Figure 3 a circular loop of wire of radius R is initially located in the plane of the page while a uniform electric field of magnitude 5 - is coming out the page in the 2 = (0,0,1) direction (represented by the "x"s). At time t = 0 the loop begins to rotate in uniform circular motion such that the top begins moving out of the page and the bottom moves into the page and the loop completes one full cycle every 5 seconds (i.e. the loop has the same orientation as that at t=0). For arbitrary time t > 0 I. Determine the unit normal of the area of the loop, n. II. Determine the vector describing the area of the loop, A. III. IV. V. Determine the flux moving through the loop as a function of time. Determine the times at which the flux is a maximum and a minimum by taking the derivative of the flux and setting it equal to zero. Use Gauss's Law to argue that the changing flux could create a current, i, which is defined as charge changing with respect to time: i=d. Give a possible mathematical value for the current. y X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Figure 3 x R