A circular single loop of wire with a diameter of 20.0 cm lies in the plane of the paper in a region of space that contains a 1.75 T magnetic field pointing out of the paper.
a) Determine the magnetic flux through this loop.
b) If the diameter of the loop changes from 20.0 cm to 10.0 cm in 0.25 seconds, what is the direction of the induced current, clockwise or counter-clockwise as seen from above? Explain your answer.
c) What is the magnitude of the induced emf that results from the diameter change in part b)?
d) What is the magnitude of the induced emf if this new smaller loop (d = 10.0 cm) is now rotated about an axis along the diameter by 90 deg in 1.50 seconds in the given magnetic field so that its normal now lies in the plane of the paper?
Flux = B*A*Cos(theta)
Induced emf = (change in flux)/change in time
A = pi*r^2
The Attempt at a Solution
part a) I have that A = pi*0.1^2 = 0.0314m^2
Flux = B*A*cos(0) = (1.75T)(0.0314m^2)cos(0) = 0.0550 Wb
part b) I said that it is clockwise because since B is increasing and out of the page, lenz's law suggests that it should therefore have B go into the page to oppose the change. By using right hand rule, fingers curl clockwise when thumb points into the page.
part c) I used induced emf = delta flux/time
induced emf = (1.75*(pi*0.05^2 - pi*0.1^2))/0.25s = 0.165 V
part d) I am not sure what angle to use for this. I think that I would have to find flux using the formula B*A*cos(theta). Any hint would be much appreciated!
*Also, am I doing the other 3 parts correctly?
*edit for part d
I tried doing it with 0 deg again and i did B*A*cos0 = 1.75*(pi*0.05^2)*cos0 = 0.0137 Wb
then i did
induced emf = (0.0137wb)/(1.5s) = 0.00913 V. Is this how I am supposed to do part d?