How Does a Changing Magnetic Field Induce EMF in a Circular Loop?

[themoleculoma]

Homework Statement

Resistance = R
Radius = r
Angle = theta
B = 2cos(2t)
Circular wire loop where magnetic field acts at theta degrees with respect to the normal of the wire loop.
Find induced current and emf in wire loop. Find induced electric field at radial distance d from center of wire loop.

Homework Equations

$$\epsilon$$ = -d$$\Phi$$/dt
I = $$\epsilon$$/R

The Attempt at a Solution

A = $$\pi$$r$$^{}2$$
$$\epsilon$$ = d(BA)/dt
= A dB/dt
= $$\pi$$r$$^{}2$$ d(2cos(2t))/dt
= -4$$\pi$$r$$^{}2$$ sin(2t) = induced emf (area not changing)

Given a magnetic field B with a constraint of 2t for $$\omega$$t, and no time, the answer must be with respect to t, correct? You can't use the frequency given by 2/2pi can you?

i = $$\epsilon$$ / R
i = -4$$\pi$$r$$^{}2$$ sin(2t) / R

Since I still don't know time I'm guessing I have to solve as a function of t?

$$\epsilon$$ = dB/dt d/2 = -2sin(2t)d

 

[Delphi51]

There should be a sin(theta) or cos(theta) in the expression for emf because only the part of B that is perpendicular to the coil causes emf.

Other than that, your calcs look good to me except for the very last line, which I don't understand at all. Leave the sin(2t) in your answers - don't try to solve for t.

 

[themoleculoma]

Oh right, I forgot that :) Still trying to figure out the last part. Thanks