Magnetic flux:

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta}}}$, where θ is the angle between the normal to area A and the direction of the magnetic field B.

The emf induced in the coil due to change in flux is given by:

$\overline{){\mathbf{\epsilon}}{\mathbf{=}}{\mathbf{n}}{\mathbf{\left|}}\frac{\mathbf{d}\mathbf{\varphi}}{\mathbf{d}\mathbf{t}}{\mathbf{\right|}}}$

**Part A**

We're told that the plane of the areas of the coil is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field, θ = 0°

In a physics laboratory experiment, a coil with 230 turns enclosing an area of 12.1 cm^{2} is rotated during the time interval 4.10×10^{-2} s from 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 5.00×10^{-5} T.

Part A

What is the total magnitude of the magnetic flux (Φ_{initial}) through the coil before it is rotated?

Express your answer numerically, in webers, to at least three significant figures.

Part B

What is the magnitude of the total magnetic flux Φ_{final} through the coil after it is rotated?

Express your answer numerically, in webers, to at least three significant figures.

Part C

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

Express your answer numerically (in volts) to at least three significant figures.

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