A radio wave transmits 1.59 W/m² average power per unit area.What is the peak value of the associated magnetic field? (μ₀ = 4π × 10−⁷ T⋅m/A and c = 3.00 × 10⁸ m/s) A)1.33E-14 T B)3.46E+1 T C)1.15E-7 T D)7.28E-5 T E)8.16E-8 T

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Quizplus · Accepted Answer

The peak value of the magnetic field (B_peak) associated with a radio wave can be calculated using the formula for the intensity (I) of an electromagnetic wave, which is given by $I = \frac{1}{2} c \epsilon_0 B_{peak}^2$, where $c$ is the speed of light, and $\epsilon_0$ is the permittivity of free space. Given that $I = 1.59 \, \text{W/m}^2$, $c = 3.00 \times 10^8 \, \text{m/s}$, and $\mu_0 = 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}$, and knowing that $\epsilon_0 \mu_0 c^2 = 1$, we can rearrange the formula to solve for $B_{peak}$. The correct calculation leads to a peak magnetic field value of approximately $1.15 \times 10^{-7} \, \text{T}$, which corresponds to choice C.

A Radio Wave Transmits 1