How to Calculate Total Charge Inside a Uniformly Charged Cylinder

How is the total charge inside a uniformly charged cylinder calculated?

That's correct. When charge is uniformly distributed with charge density rho inside a very long cylinder of radius r, it means that the charge is spread evenly throughout the volume of the cylinder. The charge density rho represents the amount of charge per unit volume.

Understanding Uniformly Charged Cylinder

Charge Density: Inside a very long cylinder with a radius r, the charge density rho is uniformly distributed. This implies that the charge is evenly spread throughout the volume of the cylinder.

Calculating Total Charge:

To calculate the total charge inside a uniformly charged cylinder, we use the formula:

Q = rho * V

Where:

  • Q = Total charge inside the cylinder
  • rho = Charge density
  • V = Volume of the cylinder

Since the cylinder is very long, we consider it to be infinite in length. The volume of the cylinder can be calculated as the product of its cross-sectional area A (given by pi * r², where r is the radius) and its length L:

V = A * L = (pi * r²) * L

Substituting the expression for V back into the equation for Q, we get:

Q = rho * (pi * r²) * L

This equation gives us the total charge inside the cylinder in terms of the charge density, radius, and length of the cylinder.

Note that this calculation assumes a uniform charge distribution throughout the entire volume of the cylinder.

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