Problem 1: Find $B_{0}$ and Intensity from $E_{0}$

Given: An EM wave has electric field E = 50 sin(ωt – kx) V/m. Find: Magnetic field amplitude $B_{0}$, and intensity I.

Step 1: Identify $E_{0}$ $E_{0}$ = 50 V/m (amplitude of the sine wave)

Step 2: Calculate $B_{0}$ using $E_{0}$/$B_{0}$ = c $B_0 = \frac{E_0}{c} = \frac{50}{3 \times 10^8} = 1.667 \times 10^{-7} \text{ T} = 166.7 \text{ nT}$

Step 3: Calculate intensity $I = \frac{1}{2}\varepsilon_0 c E_0^2 = \frac{1}{2}(8.85 \times 10^{-12})(3 \times 10^8)(50)^2$ $= \frac{1}{2}(8.85 \times 10^{-12})(3 \times 10^8)(2500)$ $= \frac{1}{2}(8.85 \times 3 \times 2500 \times 10^{-4})$ $= \frac{1}{2}(6637.5 \times 10^{-4}) = 0.3319 \approx 0.33 \text{ W/m}^2$

Answer: $B_{0}$ = $1.67 \times 10^{-7}$ T; I ≈ 0.33 W/$m^{2}$