(15) 3. Assume a particle is moving around the unit circle in the X-y plane, and that the strength of the magnetic field in the X-y plane at any given point is given by B = y sin x. If the position of the particle at time t is (X,y) = (cos t, sin t), find (using the chain rule) (a) The rate of change of the magnetic eld % at time t, in terms of x,y, and t (b) The value of % when t = 7r. dZB . (c) The second derivative W In terms of x,y, and t