91Ó°ÊÓ

In order to change the charge of an object, electrons may be removed or added. Here, electrons are removed to change the charge from \(-2.0 \, \mu \mathrm{C}\) to \(+3.0 \, \mu \mathrm{C}\). Electrons have a negative charge, approximately \(-1.6 \times 10^{-19} \, \mathrm{C}\) each. When you remove these negatively charged electrons, the overall charge of the object becomes more positive.

To determine how many electrons need to be removed, we first calculate the total required change in charge. The initial charge is negative, and we want a positive final charge. The amount of charge increase needed is \(+5.0 \, \mu \mathrm{C}\). This number tells us how much negativity we need to eliminate through electron removal.

Understanding this is key. Removing electrons, we move towards a more positive charge.

The next important step is the calculation of the charge required for this transition. The difference between the initial and final charge tells us the charge change needed. Here, the object’s charge increases from \(-2.0 \, \mu \mathrm{C}\) to \(+3.0 \, \mu \mathrm{C}\), amounting to a total change of \(+5.0 \, \mu \mathrm{C}\). This is obtained by taking the final charge minus the initial: \[3.0 \, \mu \mathrm{C} - (-2.0 \, \mu \mathrm{C}) = 5.0 \, \mu \mathrm{C}\].

This value is crucial as it reflects the net electron removal needed to achieve the desired positive charge. Using this charge change, we can determine how many electrons correspond to this amount by employing unit conversion and division by the charge of a single electron.

Before we can calculate the number of electrons removed, we need to convert the total charge change from microcoulombs to coulombs. This is because the charge of one electron is known in coulombs, and both values must be in the same units for accurate calculation.

It's essential to know that \(1 \, \mu \mathrm{C} = 10^{-6} \, \mathrm{C}\). So when converting the total charge change of \(5.0 \, \mu \mathrm{C}\), we multiply by \(10^{-6}\) to get \(5.0 \times 10^{-6} \, \mathrm{C}\).

Proper conversion ensures all calculations are aligned, giving reliable results when finding the number of electrons involved.

Significant figures are important in physics to express precision in our answers. When performing charge calculations, the final answer must reflect the significant figures based on the initial data provided. In our problem, values are given to one decimal place, so our results should match this accuracy.

After calculating that \(3.125 \times 10^{13}\) electrons are needed to change the charge, we round and express it as \(3.1 \times 10^{13}\), respecting the same decimal precision. This ensures clarity and maintains the numerical integrity of the solution throughout the process.

Such attention to detail reflects the thorough understanding and presentation of scientific data, making the results communicative and standard-compliant.