EST Shocking your friend (a) You shuffle across the rug and...

EST Shocking your friend (a) You shuffle across the rug and then place your finger near your friend’s nose, causing a small spark that transfers about $10^{-9} \mathrm{C}$ of charge from you to your friend. Determine the number of electrons transferred. (b) Estimate the fraction of electrons in your body that were transferred to the friend. Note that the electron mass is about 1/20,000 the mass of the atom—the nuclei are much more massive—and the mass of an average atom in the body is about $2 \times 10^{-26} \mathrm{kg}$. (Note: Don’t get hung up on minutia— this is a rough estimate.)

Key Concepts

Elementary Charge

This concept refers to the fundamental unit of electric charge carried by a single electron, approximately 1.6 × 10?¹? coulombs. It underpins the quantization of charge, meaning that any macroscopic charge transfer happens in discrete multiples of this elementary charge.

Charge Quantization and Calculation

Because electric charge is quantized, when a known total charge is transferred, one can determine the number of electrons that moved by dividing the total charge by the elementary charge. This basic arithmetic is a direct application of the discrete nature of charge in electromagnetism.

Order-of-Magnitude Estimation

Many physical problems, particularly those involving very small charges or large numbers of particles, are approached using order-of-magnitude estimates. These techniques simplify complex calculations by focusing on approximate scales rather than precise values, allowing for a rough, yet insightful, understanding of physical processes.

Atomic Composition and Estimation in Matter

Understanding the average mass of an atom and the corresponding number of electrons per atom is crucial for estimating the total number of electrons in a given mass of matter, such as the human body. By comparing the number of transferred electrons to the total electrons in a body—which can be approximated using the average atomic mass—one can determine the fraction of electrons involved in a transfer event.

Transcript

Please give Ace some feedback