Math Problem Statement

  1. Common static electricity involves charges ranging from nanocoulombs to microcoulombs. a. How many electrons are needed to form a charge of –2.00nC

Solution

To determine how many electrons are needed to form a charge of 2.00nC-2.00 \, \text{nC}, we can use the relationship between charge and the number of electrons.

The charge QQ is related to the number of electrons nn by the equation: Q=n×eQ = n \times e where:

  • Q=2.00nC=2.00×109CQ = -2.00 \, \text{nC} = -2.00 \times 10^{-9} \, \text{C}
  • ee is the elementary charge (the charge of a single electron), which is approximately 1.60×1019C-1.60 \times 10^{-19} \, \text{C}.

To find the number of electrons nn, we rearrange the equation: n=Qen = \frac{Q}{e}

Now, substituting the values: n=2.00×109C1.60×1019Cn = \frac{-2.00 \times 10^{-9} \, \text{C}}{-1.60 \times 10^{-19} \, \text{C}}

n=1.25×1010n = 1.25 \times 10^{10}

Thus, 1.25×10101.25 \times 10^{10} electrons are needed to form a charge of 2.00nC-2.00 \, \text{nC}.

Would you like more details or have any other questions?

Here are 5 related questions:

  1. How would the number of electrons change if the charge was 5.00nC-5.00 \, \text{nC}?
  2. What is the total charge if you have 5.00×10105.00 \times 10^{10} electrons?
  3. How does the elementary charge compare to other fundamental constants?
  4. What are practical examples of charges in microcoulombs?
  5. How is static electricity generated and why does it involve such small charges?

Tip: Remember, the sign of the charge indicates whether the particles are electrons (negative) or protons (positive).

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Math Problem Analysis

Mathematical Concepts

Electric Charge
Elementary Charge
Coulomb's Law

Formulas

Q = n * e

Theorems

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Suitable Grade Level

Advanced High School