An $800 - \mathrm { kHz }$ Sinusoidal Radio Signal Is Detected at a Point

Multiple Choice

An $800 - \mathrm { kHz }$ sinusoidal radio signal is detected at a point $6.6 \mathrm {~km}$ from the transmitter tower. The electric field amplitude of the signal at that point is $0.780 \mathrm {~V} / \mathrm { m }$ . Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the amplitude of the magnetic field of the signal at that point? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \right.$ $\mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } , c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A }$ )

A) $2.6 \mathrm { nT }$
B) $3.1 \mathrm { nT }$
C) $3.6 \mathrm { nT }$
D) $1.6 \mathrm { nT }$
E) $2.1 \mathrm { nT }$