The intensity of an electromagnetic wave is $I=0.06{\text{ W/m}}^2$. What is the maximum value of the magnetic field $B_0$ associated with this wave? (Given ${ϵ}_0=8.85\times 10^{-12}\text{ F/m}$ and $c=3\times 10^8\text{ m/s}$)

Solution

1. The intensity of an electromagnetic wave is given by $I=\frac{c{B}_0^2}{2{\mu }_0}$, where ${\mu }_0=4\pi \times 10^{-7}\text{ T m/A}$.
2. Rearranging the formula to solve for the maximum magnetic field $B_0$ gives $B_0=\sqrt{\frac{2I{\mu }_0}{c}}$.
3. Substitute the given values $I=0.06{\text{ W/m}}^2$, ${\mu }_0=4\pi \times 10^{-7}\text{ T m/A}$, and $c=3\times 10^8\text{ m/s}$ into the equation.
4. Calculate the result: $B_0=\sqrt{\frac{2(0.06)(4\pi \times 10^{-7})}{3\times 10^8}}\approx 2.0\times 10^{-8}\text{ T}$.
5. Hence the answer is (A).