Question

Electrical charge is sometimes reported in coulombs (C). On this scale, 1 electron has a charge of \(-1.6 \times 10^{-19} \mathrm{C}\). Suppose your body acquires \(-125 \mathrm{mC}\) (millicoulombs) of charge on a dry day. How many excess electrons has it acquired? (Hint: Use the charge of an electron in coulombs as a conversion factor between charge and number of electrons.)

Short answer

The body has acquired \(7.8125 \times 10^{14}\) excess electrons.

Step-by-step solution

Understand the Concepts

The charge of one electron is given as -1.6 x 10^-19 coulombs. The acquired charge by the body is -125 mC, where 1 mC (millicoulomb) is 10^-3 coulombs.

Convert millicoulombs to coulombs

Convert the charge acquired by the body from millicoulombs to coulombs by multiplying by 10^-3. Thus, -125 mC becomes -125 x 10^-3 C.

Calculate the Number of Electrons

To find the number of electrons, divide the total charge by the charge of one electron. In formula form: \( \text{Number of electrons} = \frac{\text{Total charge in C}}{\text{Charge of one electron in C}} \)

Perform the Calculation

Using the formula from step 3, calculate the number of electrons: \( \text{Number of electrons} = \frac{-125 \times 10^{-3} \text{ C}}{-1.6 \times 10^{-19} \text{ C/electron}} \)

Simplify the Calculation

After performing the division, you will find the number of excess electrons acquired by the body.

Key concepts

Coulombs

The coulomb, symbolized as C, is the standard unit of electric charge in the International System of Units (SI). It is named after the French physicist Charles-Augustin de Coulomb. One coulomb is equivalent to the charge of approximately 6.242 x 10^18 electrons.

Understanding coulombs helps us measure how much electric charge objects carry. For comparison, imagine a small object carrying a charge of 1C – it would have an enormous amount of excess or deficit electrons, which is rarely the case in everyday situations. Instead, we often deal with much smaller charges, typically expressed in millicoulombs (mC), where 1 mC is one-thousandth of a coulomb, or 10^-3 C.

Electrons

Electrons are subatomic particles with a negative electric charge. Each electron carries a charge of approximately -1.6 x 10^-19 coulombs. This tiny charge may seem insignificant, but when you get a lot of electrons together, their combined charge adds up.

The behavior of electrons is crucial to understanding electrical phenomena because they are the primary charge carriers in atoms. When an object has more electrons than protons, it has a negative charge, and when it has fewer electrons than protons, it has a positive charge. The net charge of an object is the sum of the charges of all the electrons and protons.

Electric Charge Conversion

Electric charge conversion involves converting between different units of charge (like coulombs and millicoulombs) and understanding the relationship between the charge and the number of electrons involved.

For instance, in the given exercise, the student must convert -125 millicoulombs to coulombs to understand the overall charge in standard units. This conversion is a crucial step for accurately finding the equivalent number of electrons. The conversion factor is based on the definition that 1 mC is equal to 10^-3 C.

Quantitative Problem Solving

Quantitative problem solving in physics requires a clear understanding of the fundamentals concepts and their relationships. In the context of electric charge, it involves using known values (like the charge of an electron) and given information (like total charge in coulombs) to calculate an unknown (number of electrons, in this case).

Quantitative problems often involve several conversion steps and formula manipulations. To solve these problems, one must follow the steps systematically—first by understanding the concepts, then converting to appropriate units if necessary, setting up the formulas, and finally performing the calculations to arrive at the solution.