Question 25.60: The chocolate crumb mystery. This story begins with Problem ......
The chocolate crumb mystery. This story begins with Problem 60 in Chapter 23. As part of the investigation of the biscuit factory explosion, the electric potentials of the workers were measured as they emptied sacks of chocolate crumb powder into the loading bin, stirring up a cloud of the powder around themselves. Each worker had an electric potential of about 7.0 kV relative to the ground, which was taken as zero potential. (a) Assuming that each worker was effectively a capacitor with a typical capacitance of 200 pF, find the energy stored in that effective capacitor. If a single spark between the worker and any conducting object connected to the ground neutralized the worker, that energy would be transferred to the spark. According to measurements, a spark that could ignite a cloud of chocolate crumb powder, and thus set off an explosion, had to have an energy of at least 150 mJ. (b) Could a spark from a worker have set off an explosion in the cloud of powder in the loading bin? (The story continues with Problem 60 in Chapter 26.)
(a) Equation 25-22 yields
U={\frac{1}{2}}C V^{2} (potential energy). (25-22)
U={\frac{1}{2}}C V^{2}={\frac{1}{2}}\bigl(200\times10^{-12}\ \mathrm{{{F}}}\bigr)\bigl(7.0\times10^{3}\mathrm{{{V}}}\bigr)^{2}=4.9\times10^{-3}\mathrm{{{J}}}.
(b) Our result from part (a) is much less than the required 150 mJ, so such a spark should not have set off an explosion.