A square loop (side a ) rotates in a uniform magnetic field B perpendicular to the rotation axis. What is the maximum induced EMF ( e_ max ) and the first angle (between magnetic field B and the loop normal) where it occurs?

Step-by-step solution

The magnetic flux through the loop at any instant is given by = B A = B A , where is the angle between the magnetic field and the normal to the loop area. Since the loop rotates with an angular velocity , we have = t . The area of the square loop is A = a^2 . The induced EMF is given by Faraday's law of induction: e = - d dt = - d dt (B a^2 ) = B a^2 The maximum induced EMF occurs when = 1 . The first angle where this occurs is = 90^ . The maximum induced EMF is e_ max = B a^2 . Answer: Ba^2 ; = 90^