Extra Problem A6 for 7D [just one this week]. Please upload your solution to the course website by 11:59 Tuesday 5/30/2023 Here is a problem that allows you to use Eqn. 29.7 in your R textbook. Athin conducting metal shell is placed in a constant B magnetic eld B as shown in the gure. It is rotating at angular 9 velocity 0). Two conducting support rods are \"attached" to the . (o sphere by metal \"brushes", which allows the sphere to rotate under them but the rods do not move in this problem (yet they stay in electrical contact to the sphere). a A) Construct a cartesian coordinate system with the origin at the center of the sphere, the +2 axis pointing upwards, and the +y direction pointing to the right. The rods lie in the yz plane. What is the velocity v (both magnitude and direction) for a point on the sphere in the yz plane at angle 6, measured from the positive 2 axis. B) What is the vector product of va? C) For the shortest path along the sphere between the two rods, how would you describe a short chunk ofthe path cll (in terms of the geometry and parameters given) at angle 6. Hint: you will need to determine the magnitude ofdl over a small angular chunk dB, and the y and 2 components. D) What is the EMF developed over the entire path on the sphere between the two rods? E) What is the current magnitude and direction through the vertical rod