The questions is:

A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field?

First:

I applied the the equation emf=-d(phi)/dt

 

Second:

Since we know that Phi(magnetic flux)=BA, we can say that emf=-(N)(d/dt)(BAcos(theta)). Where "theta" is equal to zero because the field is perpendicular to the normal of the area of the coil.

 

The problem that I encountered was that when you take the derivative of BAcos(theta), you get -BAsin(theta) and sin(0)=0.

 

So my question is. What am I doing wrong???

This should be in homework I think.

 

However you have shown your efforts so can you tell me what theta is?

 

There are two separate trigonometric entities. One is the angle between the field and the coil, the other is sin (t) or cos (t), where t is time not angle.

 

That is the applied field strength (not direction) varies with time according to B = B₀ sin(wt)

 

Does this help.

Yes, that helps a lot. So instead of calculating the angle theta, I calculate for omega. Which turns out to be approximately 566. Then I took the derivative of cos(566t). Once I manipulated the formula to solve for B, I ended up with B = -.059sin(566t). Thanks a bunch!