$32\mathrm{.}32$ CP $($a$)$ Estimate how long it takes to bring $1$ cup $(237$ mL$)$ of room$-$temperature water to C in a microwave oven. $($b$)$ How much heat is required to heat this water? $($c$)$ Divide the required heat by the time in part $($a$)$ to estimate the power supplied to the water by the microwaves. $($d$)$If this energy were supplied by a plane electromagnetic wave incident from one direction, and if half of the wave energy was absorbed by the water, then the average wave intensity would be the twice power estimate divided by the cross$-$sectional area of the cup seen by the wave. Use this model to estimate the average intensity of the microwaves in the oven. $($e$)$ Use Eqs. $(32\mathrm{.}29)$ to estimate the amplitude of the electric field in a microwave oven.