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A coil consists of 20 turns, with a 10cm radius (all turns are uniform).

It rotates uniformly around the z-axis at an angular speed of: w=20 rad/s

A uniform magnetic field passes along the x-axis with a magnitude of B=0.3T.

Find:

a) The induced emf at any time moment t>0 if at t=0 the coil was in the yz plane.

b) Direction of the induced current at t=0.

First, b) is easy. The answer is zero, there is no induced current at t=0 because the coil is not moving through the field yet.

For a) I started with this:

E=-N*(dB flux/ dt) (where E=emf)

Since B flux=BAcos(theta)=BAcos(wt) is sub this in to get:

E = -NBAcos(wt) d/dt

E = NBAwsin(wt) then sub in the given values for N, B, w and calculate A=pi*r^2

E = 20*.3*pi(.1m)^2*20*sin(20t)

E = 1.2pi*sin(20t) is my final answer.

Is this correct? Someone in my class has E=4pi*sin(20t)

Can someone check my answer and offer some advice?

Thanks in advance.