Magnetic flux:

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

Induced emf:

$\overline{){\mathbf{\epsilon}}{\mathbf{=}}{\mathbf{N}}\frac{\mathbf{\u2206}\mathbf{\varphi}}{\mathbf{\u2206}\mathbf{t}}}$, where N is the number of turns and t is the time of rotation.

Induced current:

$\overline{){{\mathbf{i}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{\mathbf{\epsilon}}{\mathbf{R}}}$

Joe has rolled a long electrical extension cord into a coil of radius r_{c} =11 cm with N_{c} = 16 loops. The coil of extension cord is initially lying horizontally (flat) on the floor of Joe’s garage. Joe picks up the coil and rotates it 90° counterclockwise in t_{r}= 0.85 seconds so that the coil is now vertically oriented (see figure)

Part A. If the Earth’s magnetic field has strength of 0.50 gauss and makes an angle of 20.0 degrees with the garage floor, calculate the change in magnetic flux in W_{b}, through one of the loops of the coil during the rotation

Part B. Calculate the average induced emf, in volts, in the coil during the rotation

Part C. If the extension cord has a resistance of 3.0 ohms and formed a closed circuit without any other components, calculate the induced current, in amps, in the extension cord.

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