A loop of wire with an area 1cm^2 is centered within a larger loop of area 1m^2. Apower supply is generating current through the larger loop described by the function:
I(t) = 40A * cos(2t/s * 2pi/5)
Calculate EMF at time t = 3s
Magnetic flux = BAcos(theta)
EMF = d/dt Magnetic Flux = d/dt BAcos(theta)
B = ui/2r = (u/2r) 40A * cos 2t/s * 2pi/5)
u = permeability of free space = 4pi * 10^-7
r = sqrt(area of circle/pi)
The Attempt at a Solution
Some of the work done above, I set the equation of B into the emf then took the derivative with respect to time.
EMF = 57 d/dt uA/2r cos(3t - 2pi/5)^2
EMF = 57*3* uA/2r cos(6t- 2pi/5)
I confused myself over which A I was referring to and which radius as well. Thinking about this it makes sense that A is the smaller loop's area and r is the bigger loop's radius.
Does this look correct?