Question

For a beam emerging from a filter facing a floodlight, the magnetic field is given by, $B=B_{0}sin\left(\right.kz-\omega t\left.\right)$ , where, $B_{0}=1.2\times 10^{- 8}T\text{,}k=1.2\times 10^{7}m^{- 1}\text{,}\omega =3.6\times 10^{15}s^{- 1}$ . The average intensity of the beam is $\alpha $ . Find the value of $\left[10 \alpha \right]$ , where $\left[\right]$ is the greatest integer function.

Answer 1

Comparing given equation with,
$B=B_{0}sin\left(\right.kz-\omega t\left.\right)$
$\therefore I_{av}=\frac{1}{2}\frac{B_{0}^{2} c}{\mu _{0}}$
$=\frac{1}{2}\times \frac{\left(12 \times \left(10\right)^{- 8}\right)^{2} \times 3 \times \left(10\right)^{8}}{4 \pi \times \left(10\right)^{- 7}}=\frac{270}{157}$
$=1.719Wm^{- 2}$
$\approx1.72Wm^{- 2}=\alpha $ $\ldots .$ (Rounding off to 2 decimal places)
$\left[10 \alpha \right]=\left[17 . 2\right]=17$