Calculating Volume Charge Density of a Charged Cylinder

Understanding the Problem

A solid cylinder of length L and radius R is made of an insulating material. This cylinder holds a net charge of Q that is evenly distributed throughout the cylindrical volume. We are looking to find the volume charge density, ρ, of this charged cylinder.

Calculating Volume Charge Density

To calculate the volume charge density, we use the formula:
ρ = Q / (π * R^2 * L)

Detailed Explanation

The volume of the solid cylinder is given by:
V = π * R^2 * L Therefore, the volume charge density, ρ, is defined as the total charge Q divided by the volume of the cylinder. Mathematically, we have:
ρ = Q / V = Q / (π * R^2 * L)

Final Answer

The volume charge density of the charged cylinder is given by the equation:
ρ = Q / (π * R^2 * L)

Explanation

The volume charge density, ρ, of the charged cylinder can be determined by dividing the total charge, Q, by the volume, V, of the cylinder. The volume of a cylinder can be calculated using the formula V = (π * R^2 * L). Therefore, the volume charge density is given by the equation ρ = Q / V = Q / (π * R^2 * L).

What is the formula to calculate the volume charge density of a charged cylinder?

The formula to calculate the volume charge density of a charged cylinder is ρ = Q / (π * R^2 * L), where ρ is the volume charge density, Q is the total charge, R is the radius of the cylinder, and L is the length of the cylinder.

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