You want to use your microwave oven to heat \(0.20 \mathrm{~L}\) of water from room temperature to boiling. The water is in a cup that has a radius of \(30 \mathrm{~mm}\), and you want the water to reach its boiling point in \(3.00 \mathrm{~min}\). What are the required \((a)\) average power, \((b)\) average intensity, and (c) root-mean-square electric field of the microwaves? Assume all the microwaves come in from the top and are completely absorbed by the water.