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 $\mathrm{kV}$ 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 $\mathrm{pF}$ , find the energy stored in that effective capacitor. If a single spark between the worker and any conducting object connected to the ground neutral- ized 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 $\mathrm{mJ} .$ (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 $26 .$ )

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 $\mathrm{kV}$ 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 $\mathrm{pF}$ , find the energy
stored in that effective capacitor. If a single spark between the worker and any conducting object connected to the ground neutral-
ized 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 $\mathrm{mJ} .$ (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 $26 .$ )

Key Concepts

Capacitance

Capacitance is the ability of a system to store electrical charge. In the context of the problem, each worker is modeled as a capacitor, which means that their body stores electrical energy, determined by the measured capacitance. This concept is central to understanding how much energy can be stored and eventually discharged.

Electric Potential

Electric potential, or voltage, is the measure of electric potential energy per unit charge. It is a critical concept here because the workers are charged to a high potential relative to ground. The voltage, when combined with capacitance, determines the total energy stored in the system.

Energy Stored in a Capacitor

The energy stored in a capacitor is calculated using the formula E = 1/2 CV², where C is the capacitance and V is the electric potential. This concept is vital for analyzing whether the energy released during an electrostatic discharge (spark) is sufficient to ignite a flammable material like chocolate crumb powder.

Electrostatic Discharge

Electrostatic discharge (ESD) occurs when a charged object suddenly transfers its stored energy to another object, typically through a spark. Understanding this process is important because it explains how the energy stored in the worker’s body might be rapidly released, potentially igniting combustible dust if the energy meets or exceeds a certain threshold.

Ignition Threshold

The ignition threshold refers to the minimum amount of energy required to initiate combustion in a flammable material. In the investigation, comparing the energy of the spark from the discharge with this threshold helps determine whether the spark could have been responsible for igniting the chocolate crumb powder and causing an explosion.

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