Problem 2P

For the configuration in Ex. 10.1, consider a rectangular box of length l, width w, and height h, situated a distance d above the yz plane (Fig. 10.2).

(a) Find the energy in the box at time t1 = d/c, and at t2 = (d + h)/c.

(b) Find the Poynting vector, and determine the energy per unit time flowing into the box during the interval t1 < t < t2.

(c) Integrate the result in (b) from t1 to t2, and confirm that the increase in energy (part (a)) equals the net influx.

Solution

Step 1

In this problem, we have energy in the box at time , the Poynting vector and integrate the result.