A square loop of side 0.20m is fixed along one edge so that it can rotate about that edge in a uniform magnetic field of magnitude 0.30T which is perpendicular to the axis of rotation. The loop starts from a position in which its plane is perpendicular to the field, and it rotates with a constant angular velocity of 20rad s−1 about the fixed edge.
a. (i) Derive an expression for the magnetic flux through the loop as a function of time t.
b. (ii) Calculate the average value of the magnetic flux through the loop over the first 2⋅20π seconds of rotation (i.e., during the first quarter revolution).