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Chapter 20: Problem 13

Suppose the electron and proton charges differed by one part in one billion. Estimate the net charge on your body, assuming it contains equal numbers of electrons and protons.

Short Answer

Expert verified
The net charge on your body, assuming it contains equal numbers of electrons and protons which charges differ by one part in a billion, is approximately 1.6 Coulombs.

Step by step solution

01

Understand basic concepts

First, one must understand the charges on an electron and a proton are the same but of opposite sign. So, under normal conditions, the charges cancel each other out. But, according to the exercise, assume they differ by one part in a billion.
02

Calculate imbalance

The assumption implies that the per-proton charge differs from the per-electron charge by one billionth of the charge of an electron (\( \frac{1.6 x 10^{-19} C}{1,000,000,000} \)). This will be \(1.6 x 10^{-28} C\).
03

Determine the number of particles

Charge is quantized - it comes in discrete units. Here, the number of particles in human body would be on the order of \(10^{28}\) (roughly, this number is a good approximation of Avogadro's number \(6.022 x 10^{23}\) times the number of kilograms in a human body).
04

Multiply charge difference and number of particles

The net charge on a body will be this difference in charges - \(1.6 x 10^{-28} C\) per particle - multiplied by the total number of particles, which is in the order of \(10^{28}\). Multiplying these, we get a net charge of approx. \(1.6 C\).

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