a solenoid has 450 loops, each of radius 0.0254 m. the field increases from 0 t to 3.00 t in 1.55 s. what is…

Explanation:

Step1: Calculate the area of one loop

The area of a circle is $A = \pi r^{2}$. Given $r = 0.0254$ m, so $A=\pi\times(0.0254)^{2}\text{ m}^2$.

Step2: Calculate the total magnetic - flux change

The magnetic - flux through one loop is $\varPhi=BA$. The total number of loops is $N = 450$. The change in magnetic field $\Delta B=3.00 - 0=3.00$ T. The total change in magnetic - flux $\Delta\varPhi_{total}=N\times\Delta B\times A=N\times\Delta B\times\pi r^{2}$.

Step3: Calculate the induced EMF

According to Faraday's law of electromagnetic induction, $\epsilon=-\frac{\Delta\varPhi_{total}}{\Delta t}$. Since we are interested in the magnitude, $\epsilon=\frac{N\times\Delta B\times\pi r^{2}}{\Delta t}$. Substitute $N = 450$, $\Delta B = 3.00$ T, $r = 0.0254$ m and $\Delta t=1.55$ s into the formula. [ \begin{align*} \epsilon&=\frac{450\times3.00\times\pi\times(0.0254)^{2}}{1.55}\ &=\frac{450\times3.00\times\pi\times0.00064516}{1.55}\ &=\frac{450\times3.00\times0.00202719}{1.55}\ &=\frac{2.7367065}{1.55}\ &\approx1.77\text{ V} \end{align*} ]

Answer:

$1.77$ V