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How to Calculate the Electric Charge of a Volume

Electric charge is carried in discrete packages. Under normal circumstances, negative electric charge is carried by electrons and positive electric charge is carried by protons. So when charge is collected together, it's not smeared together like a jar of peanut butter, but more like a cup of sugar, with tiny particles bumping up against each other, leaving some space between. But since electrons and protons are so small, for most practical problems you can assume the charge is evenly spread throughout space.

Instructions

- 1
  Determine the total charge of a region and the total volume of a region. As an example, a uniformly-charged sphere could have a radius of 2 cm and a charge of 1.6 x 10^-13 coulombs.
- 2
  
  In the early days of learning about electricity, people collected charge in many different ways.
  
  Calculate the average charge density. The average density is the total charge divided by the volume. For the example, the volume is (4/3) x pi x radius^3, which is 33.5 cm^3. The charge divided by the volume is 4.8 x 10^-15 coulombs / cm^3.
- 3
  Compute the volume of the region of interest. For the example problem, the volume of interest could be a 1 mm thick shell centered on a 1 cm radius. The volume of that region is (4/3) x pi x (1.05^3 - 0.95^3) which is 1.3 cm^3.
- 4
  Multiply the volume of interest times the charge density calculated in Step 2. In the example, this becomes (4.8 x 10^-15 coulombs / cm^3) x 1.3 cm^3, which is 6.2 x 10^-15 coulombs.

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