John is pedaling his bike down the street perpendicular to the earth’s magnetic field of 5.5 x 10^-5 T. QUESTION CONTINUED IN DESCRIPTION!!!!

Question

John is pedaling his bike down the street perpendicular to the earth’s magnetic field of 5.5 x 10^-5 T. What is the induced voltage in one metal rim of the bicycle if the wheel has an area of 1.13 m^2 and he takes 2.0 s to make a 900 degrees turn into a northbound street?

Answer 1

Faraday’s law of induction can be written as 

 V = - (d/dt) B A cos(theta) = - B A sin(theta) d(theta)/dt

Where BA cos(theta) is the magnetic flux penetrating the wheel. In this problem, the angle theta starts at zero and reaches pi/2 after 2 sec. Thus d (theta) dt = pi/4

Carrying out the derivative and ignoring the minus sign gives

 V = 4.88E-5 sin(theta) = 4.88E-5 sin(pi t /4)

 The value of V depends on time, but at the end of the turn the value is 4.488E-5 volt