Voyager 1 is currently the furthest human-made object from Earth, at a distance of 21.2 billion (21.2  109) km, which is literally the edge of the Solar System. Onboard, it relays data to Earth via a 22.4 W radio, which transmits at a frequency of 8.42 GHz. The NASA Deep Space Network uses radio antenna dishes that are literally hundreds of feet in diameter to detect these faint signals from Voyager 1. The one at Goldstone, California, is 70 meters in diameter. Assume that dish is circular (it's actually parabolic) and its plane is oriented perpendicular to the Voyager 1 signal wave direction.
1. Calculate the power that an antenna on Earth would receive from Voyager 1. Again, show your work, and pay attention to sig figs and units. You may ignore any effects due to interplanetary dust or the Earth's atmosphere.
However, suppose you are trying to detect them yourself on a homemade loop antenna, 7.50 cm in diameter. Assume that the EM wave that Voyager 1 broadcasts is aligned so that the direction of its magnetic field is perpendicular to the plane of your loop.
2. Why is the magnetic field being perpendicular to the plane of your antenna loop ideal for receiving the probe's signals? You will have to recall a bit of Physics 222 (electricity and magnetism) to answer this. Describe (or draw) how the sinusoidal wave of the magnetic field interacts with the wire loop.
3. What is the maximum induced EMF in your loop? Will this be detectable by the equipment you've seen on Tinkercad?