Halliday, Resnick & Walker — Capacitance: Problem 20

20 As a safety engineer, you must evaluate the practice of storing flammable conducting liquids in nonconducting containers. The company supplying a certain liquid has been using a squat, cylindrical plastic container of radius \( r = 0.20 \text{ m} \) and filling it to height \( h = 10 \text{ cm} \), which is not the container’s full interior height (Fig. 25-25). Your investigation reveals that during handling at the company, the exterior surface of the container commonly acquires a negative charge density of magnitude \( 2.0 \text{ \mu C/m}^2 \) (approximately uniform). Because the liquid is a conducting material, the charge on the container induces charge separation within the liquid. (a) How much negative charge is induced in the center of the liquid’s bulk? (b) Assume the capacitance of the central portion of the liquid relative to ground is \( 50 \text{ pF} \). What is the potential energy associated with the negative charge in that effective capacitor? (c) If a spark occurs between the ground and the central portion of the liquid (through the venting port), the potential energy can be fed into the spark. The minimum spark energy needed to ignite the liquid is \( 10 \text{ mJ} \). In this situation, can a spark ignite the liquid?