Given:
The number of turns is,
[tex]n=120[/tex]The diameter of the coil is
[tex]\begin{gathered} d=9.604\text{ cm} \\ =9.604\times10^{-2}\text{ m} \end{gathered}[/tex]The angle of the magnetic field with the coil is
[tex]\theta=12\degree[/tex]The change in a magnetic field is from
[tex]0.316\text{ T to 5.553 T}[/tex]in
[tex]t=98.254\text{ s}[/tex]To find:
The induced emf
Explanation:
The induced emf in the coil is,
[tex]\xi=-nA\frac{dB}{dt}cos\theta[/tex]Here, the area of the coil is,
[tex]\begin{gathered} A=\pi\frac{d^2}{4} \\ =\pi\times\frac{(9.604\times10^{-2})^2}{4} \\ =7.244\times10^{-3}\text{ m}^2 \end{gathered}[/tex]The induced emf is,
[tex]\begin{gathered} \xi=-120\times7.244\times10^{-3}\times\frac{5.553-0.316}{98.254}cos12\degree \\ =-0.045\text{ V} \end{gathered}[/tex]Hence, the induced emf is 0.045 V.
