You are using an antenna consisting of a single loop of wire of radius 15.0 cm to detect electromagnetic waves for which E_rms = 0.200 V/m.If the wave frequency is 600 kHz,the rms value of the emf induced in the loop is approximately A)32.1 $\mu$V B)84.3 $\mu$V C)66.7 $\mu$V D)178 $\mu$V E)643 $\mu$V

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Quizplus · Accepted Answer

The rms value of the emf induced in the loop can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf ($\epsilon$) in a loop is equal to the rate of change of magnetic flux through the loop. For a loop of radius $r$ in a uniform magnetic field that changes sinusoidally with time, the induced emf can be calculated as $\epsilon = 2\pi^2 r^2 f B_{\text{rms}}$, where $f$ is the frequency of the electromagnetic wave and $B_{\text{rms}}$ is the rms value of the magnetic field, which can be related to the electric field ($E_{\text{rms}}$) in an electromagnetic wave by $B_{\text{rms}} = E_{\text{rms}}/c$, with $c$ being the speed of light ($3 \times 10^8$ m/s).Given:- $E_{\text{rms}} = 0.200$ V/m- $r = 15.0$ cm = 0.15 m- $f = 600 \times 10^3$ HzFirst, calculate $B_{\text{rms}}$:$$B_{\text{rms}} = \frac{E_{\text{rms}}}{c} = \frac{0.200}{3 \times 10^8} \approx 6.67 \times 10^{-10} \text{T}$$Then, calculate the induced emf ($\epsilon$):$$\epsilon = 2\pi^2 (0.15)^2 (600 \times 10^3) (6.67 \times 10^{-10})$$$$\epsilon \approx 66.7 \mu V$$Therefore, the correct answer is approximately 66.7 μV, which corresponds to choice C.

You Are Using an Antenna Consisting of a Single Loop μ\muμ

You Are Using an Antenna Consisting of a Single Loop $\mu$