1. The problem statement, all variables and given/known data (ignore the suggested problems for test 3.) If for whatever reason the image doesn't load the given's are that: The area is 25pi(.125m)^2 (A circular coil with 25 turns and a radius of 12.5cm.) The magnetic field varies with time and is: (1.5T/s)t I hat + (3.33T-(2.25(T/s^2)t^2))J hat -(2.10T)k hat The Area lies flat on the xz plane. 2. Relevant equations EMF=Acos(phi)(db/dt) (as only the magnetic field varies with time. 3. The attempt at a solution Area has already been given. db/dt=(1.5T/s)I hat -(4.5T/s)t J hat The problem arises when I try to calculate phi. My first instinct was to use phi as the angle between the normal of the area and db/dt (rather than B) but this was incorrect. I know now that we can calculate phi with the following formula: B dot A=BAcos(phi) As the normal to the area lies purely in the J hat direction BxAx and BzAz are both zero. Which leaves us with: ByAy=BAcos(phi) The problem is that the magnetic field we're given varies with time. How do we remove this dependency (if we even have to) to use this formula to calculate? My first instinct is that we turn this: (1.5T/s)t I hat + (3.33T-(2.25(T/s^2)t^2))J hat -(2.10T)k hat Into this: (1.5T/s)s I hat + (3.33T-(2.25(T/s^2)s^2))J hat -(2.10T)k hat Leaving us with: (1.5T)I hat + (1.08T)J hat -(2.10T)k hat But I'm unsure whether or not this is actually correct.