Question

Figure 25.16 (which looks like a horizontal bar with three rows of little blue arrows pointing in the upwards direction through the bar) shows a 100-turn coil of wire of radius 12cm in a 0.15T magnetic field. The coil is rotated 90 degrees in 0.30 s, ending up parallel to the field. What is the average emf induced in the coil as it rotates?

Answer 1

Initially magnetic field $\vec{B}$ and $\vec{A}$ are parallel.

so magnetic flux initially is $\phi_i=N\pi\,R^2\,B=100\times\3.14\times(12\times10^{-2})^2\times0.15=0.67824$

finally magnetic field $\vec{B}$ and $\vec{A}$ are perpendicular

$\phi_f=0$

time taken = 0.30 s

average EMF induced = $\varepsilon=-\frac{\Delta\,\phi}{\Delta\,t}=\frac{\phi_i-\phi_f}{\Delta\,t}=\frac{0.67824}{0.30}=2.26\,V$