Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016 N·m2/C at the planet's surface. Calculate:(c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.

Verified step by step guidance

1. Understand that the electric flux (Φ) through a closed surface is related to the charge enclosed (Q) by Gauss's Law, which is given by the formula: Φ = Q/ε₀, where ε₀ is the permittivity of free space (approximately 8.85 × 10⁻¹² C²/N·m²).
2. Rearrange Gauss's Law to solve for the total charge (Q) on Mars: Q = Φ × ε₀. Substitute the given electric flux value into this equation to find the total charge.
3. Recognize that the charge density (σ) is defined as the charge per unit area. Therefore, σ = Q/A, where A is the surface area of Mars.
4. Calculate the surface area (A) of Mars using the formula for the surface area of a sphere: A = 4πr². Use the known radius of Mars, which is approximately 3,390,000 meters.
5. Substitute the values of Q and A into the charge density formula to find the charge density on Mars: σ = Q/A. This will give you the charge density in units of C/m².

Key Concepts

Electric Flux

Electric flux is a measure of the electric field passing through a given area. It is calculated as the product of the electric field and the area perpendicular to the field lines. In this context, it helps quantify the electric field generated by Mars, which is crucial for determining the charge distribution on its surface.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the total electric flux is equal to the enclosed charge divided by the permittivity of free space. This principle is essential for calculating the charge density on Mars by using the given electric flux value.

Charge Density

Charge density refers to the amount of electric charge per unit area on a surface. It is calculated by dividing the total charge by the surface area. Understanding charge density is crucial for determining how the electric charge is distributed across Mars's surface, given the assumption of uniform distribution.