Question

a coil has 290 turns enclosing an area of 11.2 cm². in a physics laboratory experiment, the coil is rotated during the time interval 0.42 s from a position in which the plane of each turn is perpendicular to earths magnetic field to one in which the plane of each turn is parallel to the field. the magnitude of earths magnetic field at the lab location is 5.40×10⁻⁵ t. part c what is the magnitude of the average emf induced in the entire coil? express your answer in volts. view available hint(s)

Explanation:

Step1: Calculate the change in magnetic flux

The formula for magnetic flux is $\varPhi = BA\cos\theta$. Initially, $\theta_1 = 0^{\circ}$ (perpendicular), so $\varPhi_1=BA$. Finally, $\theta_2 = 90^{\circ}$ (parallel), so $\varPhi_2 = 0$. The change in flux $\Delta\varPhi=\varPhi_2-\varPhi_1=-BA$.
Given $B = 5.40\times10^{-5}\text{ T}$, $A=11.2\text{ cm}^2=11.2\times10^{-4}\text{ m}^2$, $N = 290$, $\Delta t=0.42\text{ s}$.
$\Delta\varPhi=- 5.40\times10^{-5}\times11.2\times10^{-4}$

Step2: Use Faraday's law

Faraday's law of electromagnetic induction is $\mathcal{E}=-N\frac{\Delta\varPhi}{\Delta t}$.
Substitute the values:
$\mathcal{E}=290\times\frac{5.40\times10^{-5}\times11.2\times10^{-4}}{0.42}$
First calculate $5.40\times10^{-5}\times11.2\times10^{-4}=6.048\times10^{-8}$
Then $\frac{6.048\times10^{-8}}{0.42}=1.44\times10^{-7}$
Finally, $290\times1.44\times10^{-7}=4.176\times10^{-5}$

Answer:

$4.2\times10^{-5}\text{ V}$