a solenoid with 625 loops, each with area 4.34*10^-4 m^2, is originally parallel to a 0.225 t magnetic…

Explanation:

Step1: Recall Faraday's law

$\epsilon=-N\frac{\Delta\Phi}{\Delta t}$, where $\epsilon$ is the induced EMF, $N$ is the number of loops, $\Delta\Phi$ is the change in magnetic - flux, and $\Delta t$ is the time interval.

Step2: Calculate the initial and final magnetic - flux

The magnetic - flux is given by $\Phi = B\cdot A\cdot\cos\theta$. Initially, $\theta_1 = 0^{\circ}$ (parallel), so $\Phi_1=B\cdot A\cdot\cos(0^{\circ})=B\cdot A$. Finally, $\theta_2 = 90^{\circ}$ (perpendicular), so $\Phi_2=B\cdot A\cdot\cos(90^{\circ}) = 0$. Then $\Delta\Phi=\vert\Phi_2-\Phi_1\vert=B\cdot A$.

Step3: Substitute values into Faraday's law

We know that $N = 625$, $B = 0.225\ T$, $A=4.34\times10^{-4}\ m^{2}$, and $\Delta t = 0.166\ s$. $\epsilon=N\frac{\Delta\Phi}{\Delta t}=N\frac{B\cdot A}{\Delta t}$. Substitute the values: $\epsilon = 625\times\frac{0.225\times4.34\times10^{-4}}{0.166}$ First, calculate the numerator: $0.225\times4.34\times10^{-4}=9.765\times10^{-5}$. Then, $625\times9.765\times10^{-5}=0.06103125$. Finally, $\epsilon=\frac{0.06103125}{0.166}\approx0.368\ V$.

Answer:

$0.368$