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Chapter 15: Problem 11

Write the electric charge density \(3 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3}\) using base units only, and without the use of a negative exponent or a decimal point.

Short Answer

Expert verified
Question: Rewrite the given electric charge density, \(3 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3}\), in base units without using a negative exponent or a decimal point. Answer: \(\frac{3 \mathrm{C}}{10^{4} \mathrm{m}^3}\)

Step by step solution

01

Convert the electric charge density to base units

To convert the given electric charge density, \(3 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3}\), into base units, we need to know that the charge unit is coulombs (C) and the length unit is meters (m). So the given electric charge density is already in base units.
02

Rewrite the electric charge density without negative exponent

To rewrite the given electric charge density, \(3 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3}\), without using a negative exponent or a decimal point, we can write \(10^{-4}\) as a fraction. This is done by moving the negative exponent to the denominator, so we get \(10^{4}\) in the denominator: $$ 3 \times 10^{-4} \mathrm{C} / \mathrm{m}^{3} = \frac{3 \mathrm{C}}{10^{4} \mathrm{m}^3}. $$
03

Rewrite the electric charge density without using any decimals

The given electric charge density is already without any decimals. So the final answer of the electric charge density in base units without using a negative exponent or a decimal point is: $$ \frac{3 \mathrm{C}}{10^{4} \mathrm{m}^3}. $$

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