Figure 1: Question 1 1. A square loop of wire (side length a) is rotating in the counter-clockwise direction (when viewed from above) at a constant angular velocity @ in a uniform magnetic field B = B x, where the r-axis points to the right on the page as shown in Figure ??. Assume the plane of the loop is parallel to the field as shown in the figure at time t = 0. (a) Find the magnetic flux through the loop as a function of time. [Hint: The angle between the plane of the loop and the x-axis is o = wt.] (b) Find the induced emf in the loop as a function of time. (c) At what times will the induced current change direction? (Think carefully about Lenz's Law: the direction of the current in this loop is determined by whether the flux is increasing or decreasing - at what times does that change?) 2. A long solenoid of radius a with n turns per unit length carries a current I (t) = kt, where k > 0 is a constant. A circular loop of wire of radius b > a with resistance R is looped around the solenoid. Assume both the solenoid and wire loop are centered on the z-axis. (a) Find the magnitude of the induced current in the loop of wire. (b) Assume the current in the solenoid flows in the + $ direction. In what direction is the induced current in the loop of wire? (Give the unit vector with appropriate sign.) Explain your