Magnetic flux through coiled wire

[Dr. Philgood]

Homework Statement

A circular coil has 25 turns and a radius of 5 cm. It is at the equator, where the earth’s magnetic field is 0.7G north. Find the magnetic flux through the coil when its plane is (a) horizontal, (b) vertical with its axis pointing north, (c) vertical with its axis pointing east, and (d) vertical with its axis making an angle of 30 degrees with north.

Homework Equations

\Phi =\int B\cdot da

The Attempt at a Solution

I understand the magnetic flux part basically is equal to (magnetic field)*(number of turns)*(area)*(cos(θ) in this case equaling (7*10^-5)(25)(Pi*(.05^2))(cosθ) and both A) and B) make sense with cos(90) equaling zero for A) and cos(0) equaling 1 for B). But, C) is where I'm confused.

C) I would assume that with the magnetic field pointing north and the axis pointing east the angle between them should be 90°. Though this is wrong, the correct angle between them is apparently 30°. My question is why is this angle 30° and not 90°?

 

[BruceW]

You don't really multiply by the number of turns to get magnetic flux. But you will need to multiply by the number of turns if you want to find the emf over the whole coil. So I guess it doesn't matter if you do the multiplication now.

About the answer for part c, you're right, the angle is 90 degrees. Maybe you were looking at the answer to part d when you saw 30 degrees?