# Homework Help: Magnetic flux through coiled wire

1. Mar 27, 2012

### Dr. Philgood

1. The problem statement, all variables and given/known data

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.

2. Relevant equations
\Phi =\int B\cdot da

3. 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°?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 1, 2012

### 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?

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