If cube of side 5 cm has charge 6 microcoulombs then surface density is

To find the surface charge density of a cube with a given charge, we first need to understand what surface charge density means. Surface charge density is defined as the amount of charge per unit area on a surface. In this case, we have a cube with a total charge of 6 microcoulombs and we need to calculate the surface charge density based on the surface area of the cube.

Calculating the Surface Area of the Cube

The formula for the surface area (A) of a cube is:

• A = 6 * (side length)²

Given that the side length of the cube is 5 cm, we can substitute this value into the formula:

• A = 6 * (5 cm)²
• A = 6 * 25 cm²
• A = 150 cm²

Converting Units

Before we proceed to calculate the surface charge density, it's helpful to convert the area into square meters, as the standard unit for surface charge density is coulombs per square meter (C/m²). Since 1 cm² is equal to 0.0001 m², we can convert:

• A = 150 cm² * 0.0001 m²/cm² = 0.015 m²

Calculating Surface Charge Density

Now that we have the surface area in square meters, we can calculate the surface charge density (σ) using the formula:

• σ = Q / A

Where Q is the total charge and A is the surface area. The total charge given is 6 microcoulombs, which is equal to 6 x 10^-6 coulombs. Substituting the values we have:

• σ = (6 x 10^-6 C) / (0.015 m²)
• σ = 4 x 10^-4 C/m²

Final Result

Thus, the surface charge density of the cube is 4 x 10^-4 C/m². This value indicates how much charge is distributed over each square meter of the cube's surface, providing insight into the electric field that might be generated around it.