Intensity of sunlight is observed as 0.092 Wm$$^{-2}$$ at a point in free space. What will be the peak value of magnetic field at that point? ($$\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)

The intensity of an electromagnetic wave is related to the peak electric field by: $$I = \frac{1}{2}\varepsilon_0 c E_0^2$$

And the peak magnetic field is related to the peak electric field by: $$B_0 = \frac{E_0}{c}$$

Combining these: $$I = \frac{1}{2}\varepsilon_0 c \cdot (B_0 c)^2 = \frac{1}{2}\varepsilon_0 c^3 B_0^2$$

Solving for $$B_0$$: $$B_0 = \sqrt{\frac{2I}{\varepsilon_0 c^3}}$$

Substituting the values: $$I = 0.092 \text{ W m}^{-2}$$, $$\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{N}^{-1}\text{m}^{-2}$$, $$c = 3 \times 10^8 \text{ m s}^{-1}$$: $$B_0 = \sqrt{\frac{2 \times 0.092}{8.85 \times 10^{-12} \times (3 \times 10^8)^3}}$$

Computing the denominator: $$(3\times10^8)^3 = 27\times10^{24}$$ $$8.85\times10^{-12} \times 27\times10^{24} = 238.95\times10^{12} = 2.3895\times10^{14}$$

$$B_0 = \sqrt{\frac{0.184}{2.3895\times10^{14}}} = \sqrt{7.699\times10^{-16}} = 2.775\times10^{-8} \text{ T} \approx 2.77\times10^{-8} \text{ T}$$