An upright rectangular loop of height a and width b has a lightbulb attached to it, with some resistance R. It is immersed in a constant magnetic field with magnitude Bo, pointing into the page. Now you want to turn on the lightbulb by using Faraday's law of electromagnetic induction. a. Since the magnetic field is fixed and the dimensions of the loop are also fixed, the only way to change the magnetic flux in the loop is to rotate it, let's say at some angular speed w. Write down the value of the magnetic flux as a function of time. b. Calculate the electromotive force and solve for the induced current. What is the direction of the induced current? c. Solve for the power delivered in the lightbulb. d. You may notice that the power delivered in the lightbulb varies as a function of time t. At what values of t will the lightbulb shine the brightest?

An upright rectangular loop of height a and width b has a lightbulb attached to it, with some resistance R. It is immersed in a constant magnetic field with magnitude Bo, pointing into the page. Now you want to turn on the lightbulb by using Faraday's law of electromagnetic induction. a. Since the magnetic field is fixed and the dimensions of the loop are also fixed, the only way to change the magnetic flux in the loop is to rotate it, let's say at some angular speed w. Write down the value of the magnetic flux as a function of time. b. Calculate the electromotive force and solve for the induced current. What is the direction of the induced current? c. Solve for the power delivered in the lightbulb. d. You may notice that the power delivered in the lightbulb varies as a function of time t. At what values of t will the lightbulb shine the brightest?