Question

In a physics laboratory experiment, a coil with 230 turns enclosing an area of 12.1 cm2 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 ( ?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 ?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.

 

Answer 1

Part-A

The total magnitude of the magnetic flux \(\phi_{\text {intial }}\) through the coil before it is rotated is,

$$ \begin{aligned} \phi_{\text {Initial }} &=B A \sin \theta \\ &=\left(5.00 \times 10^{-5} \mathrm{~T}\right)\left(12.1 \mathrm{~cm}^{2}\right)\left(\frac{10^{-4} \mathrm{~m}^{2}}{1 \mathrm{~cm}^{2}}\right) \sin 90^{\circ} \\ \phi_{\text {Initial }} &=6.05 \times 10^{-8} \mathrm{~Wb} \end{aligned} $$

Part-B

The magnitude of the total magnetic flux \(\phi_{\text {Final }}\) through the coil after it is rotated is,

$$ \begin{aligned} \phi_{\text {Final }} &=B A \sin \theta \\ &=\left(5.00 \times 10^{-5} \mathrm{~T}\right)\left(12.1 \mathrm{~cm}^{2}\right)\left(\frac{10^{-4} \mathrm{~m}^{2}}{1 \mathrm{~cm}^{2}}\right) \sin 0^{\circ} \\ \phi_{\text {Final }} &=0 \mathrm{~Wb} \end{aligned} $$

Part-C

The magnitude of the average emf induced in the coil is,

$$ \begin{aligned} \varepsilon &=N \frac{\Delta \phi}{\Delta t} \\ &=N\left(\frac{\phi_{\text {Initial }}-\phi_{\text {iinal }}}{\Delta t}\right) \\ &=(230 \text { turns })\left(\frac{6.05 \times 10^{-8} \mathrm{~Wb}-0 \mathrm{~Wb}}{4.10 \times 10^{-2} \mathrm{~s}}\right) \\ \varepsilon &=3.39 \times 10^{-4} \mathrm{~V} \end{aligned} $$

Part A

\(6.05 \times 10^{-8} \mathrm{~Wb}\)

Part B

\(0 \mathrm{~Wb}\)

Part C

\(3.39 \times 10^{-4} \mathrm{~V}\)