You want to build a portable device that can detect pirate radio stations broadcasting at about \(50 \mathrm{~W}\) of power a few miles from your beachfront home. You have a \(0.60-\mathrm{m}\) diameter bowl you might use as antenna dish, but you are worried that your amplifier input will require a signal of at least \(0.10 \mu \mathrm{W}\).