Question

Problem #6

A company supplying flammable liquid uses a plastic cylinder of radius r = 0.20 m and filled to a height h = 10. cm. During handling, the container develops a uniform surface charge density σ = -2.0 μC/m2. Because the liquid is a conductor, the charge on the container induces charge separation in the liquid. How much negative charge is induced in the center of the liquid’s bulk? Assume the capacitance of the liquid relative to the ground is 35. pF. What is the potential energy stored in that effective capacitor? If a spark occurs, the potential energy can be fed into the spark. The minimum spark needed to ignite the liquid is 10. mJ. In this situation, can the spark ignite the liquid?

Answer 1

we can find the surface area of cylinder as

A = 2rh + r²

A = 2 * 0.2 * 0.1 + * 0.2²

A = 0.2513 m²

so,

q = A

q = -2e- 6 * 0.2513

q = - 0.5 uC

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energy stored is given as

U = q² / 2C

U = 0.5e-6² / 2 * 35e-12

U = 3.61e-3 J

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minimum spark energy needed = 10 mJ = 10e-3 J

we got U = 3.61e-3

so,

factor = 10e-3 / 3.61e-3

factor = 2.77

so,

most probably spark will not cocur