Some engineers breadboard a device by scavenging a $1$ kW magnetron from an old microwave oven and connecting it to a horn antenna with $10$ dBi of gain. Assume the magnetron emanates a signal at $915$ MHz$.$ What is the maximum radiation power density at a distance of $2000$ meters?$$ Assume that the horn is pointed toward the zenith so that you can assume free space propagation conditions.$$Express your answer in microwatts per square meter.