As a person moves about in a dry environment, electric...

As a person moves about in a dry environment, electric charge accumulates on his body. Once it is at high voltage, either positive or negative, the body can discharge via sometimes noticeable sparks and shocks. Consider a human body well separated from ground, with the typical capacitance $150 \mathrm{pF}$. (a) What charge on the body will produce a potential of $10.0 \mathrm{kV} ?$ (b) Sensitive electronic devices can be destroyed by electrostatic discharge from a person. A particular device can be destroyed by a discharge releasing an energy of $250 \mu \mathrm{J}$. To what voltage on the body does this correspond?

Key Concepts

Capacitance

Capacitance is a measure of a system's ability to store charge per unit voltage. In this context, the human body is modeled as a capacitor with a specific capacitance, meaning that the amount of electrical charge it can store is directly proportional to the voltage across it. This concept is central to understanding phenomena such as electrostatic discharge, where the stored charge can suddenly be released when a conductive path is provided.

Electric Potential (Voltage)

Electric potential, or voltage, is the measure of the potential energy per unit charge in an electric field. It represents the force that drives the movement of charge, and in the context of electrostatic discharge from the human body, high voltage results from the accumulation of charge. Knowing the voltage is crucial for calculating both the stored charge (using Q = CV) and the energy released during discharge.

Relationship Between Charge, Capacitance, and Voltage

The relationship among charge, capacitance, and voltage is described by the equation Q = CV, where Q represents the charge, C is the capacitance, and V is the voltage. This fundamental relationship is used to determine how much charge is stored on a capacitor-like body when a certain voltage is applied, and it forms the basis of analyzing electrostatic charge accumulation in objects, including the human body.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the formula E = 1/2 CV², which relates the capacitance and the voltage to the stored energy. This concept is essential for understanding how much energy is available during an electrostatic discharge, which can have implications for sensitive electronic devices. It quantifies the potential damage that might occur if a discharge releases sufficient energy.

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