Magnetic Flux and Induced EMF in a Coil

[erik-the-red]

In a physics laboratory experiment, a coil with 210 turns enclosing an area of 12.7 cm^2 is rotated during the time interval 3.70 \cdot 10^{−2} sfrom a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 5.20 \cdot 10^{−5} T.

What is the magnitude of the average emf induced in the coil?

I've already found the total magnitude of the magnetic flux through the coil before and after rotation.

Since the magnitude after rotation is zero, the change in magnetic flux is merely the negative of the initial magnetic flux.

I use the equation {\cal{E}} = - N \frac{d \Phi_1}{dt} = - N \frac{\Delta \Phi_1}{\Delta t}.

Plugging in, I get -\frac{210 \cdot (-1.39 \cdot 10^{-5})}{3.70 \cdot 10^{-2}}.

The negatives cancel out, leaving me with a positive answer.

But, my answer is wrong.

What happened?

[OlderDan]

In a physics laboratory experiment, a coil with 210 turns enclosing an area of 12.7 cm^2 is rotated during the time interval 3.70 \cdot 10^{−2} sfrom a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 5.20 \cdot 10^{−5} T.

What is the magnitude of the average emf induced in the coil?

I've already found the total magnitude of the magnetic flux through the coil before and after rotation.

Since the magnitude after rotation is zero, the change in magnetic flux is merely the negative of the initial magnetic flux.

I use the equation {\cal{E}} = - N \frac{d \Phi_1}{dt} = - N \frac{\Delta \Phi_1}{\Delta t}.

Plugging in, I get -\frac{210 \cdot (-1.39 \cdot 10^{-5})}{3.70 \cdot 10^{-2}}.

The negatives cancel out, leaving me with a positive answer.

But, my answer is wrong.

What happened?
How did you calculate the flux?

[erik-the-red]

The first part of the question asked:

What is the total magnitude of the magnetic flux (\Phi_i) through the coil before it is rotated?

I used the equation \Phi_i = B \cdot A \cdot \cos(\phi). My answer of 1.39e(-5) is correct.

[OlderDan]

The first part of the question asked:

What is the total magnitude of the magnetic flux (\Phi_i) through the coil before it is rotated?

I used the equation \Phi_i = B \cdot A \cdot \cos(\phi). My answer of 1.39e(-5) is correct.
????

The initial angle in the problem you stated is 0; cos(0) = 1.

B*A*cos(0) = 5.2e-5T*12.7cm^2*(1m/100cm)^2=6.6e-8Tm^2

Where have I gone wrong?

[erik-the-red]

There are actually 10,000 square centimeters in one square meter. This is a problem from an online assignment. I know the first and second parts are correct.

The third part is still puzzling me.

[OlderDan]

There are actually 10,000 square centimeters in one square meter. This is a problem from an online assignment. I know the first and second parts are correct.

The third part is still puzzling me.
(100cm/m)^2 is 10,000 cm^2/m^2

I think I see the problem.

1.39e-5 = 6.6e-8*210

In the earlier part of the problem you already multiplied the flux times the number of turns. Now you are doing it again to calculate the emf. I don't know what the earlier question was, but you only get to multiply by N once to calculate emf.

[erik-the-red]

OlderDan, thanks!