Question

If the potential on the surface of the sphere is 2200_V and the capacitance is 6.56 x 10 1. what is the surface charge density? The Coulomb constant is 8.98755 x 10' N.mp/cº. Answer in units of nC/m"".

Answer 1

To calculate the surface charge density of a sphere given its potential and capacitance, one must find the total charge using Q = CV, then determine the radius to find the area of the sphere and divide the charge by the area.

Step-by-step explanation:

The problem pertains to calculating the surface charge density (σ) of a sphere given its potential (V) and capacitance (C). To find the surface charge density, we use the relationship between charge (Q), potential (V), and capacitance (C), which is Q = CV. Once the total charge on the sphere's surface is calculated, σ can be found by dividing this charge by the area of the sphere. The area of a sphere is given by A = 4πr², where r is the radius of the sphere. The radius can be determined from the capacitance as follows: C = 4πε₀r, with ε₀ being the vacuum permittivity (8.854 x 10⁻¹² C²/N·m²). We can then proceed to calculate the total charge (Q = CV), find the radius of the sphere from the capacitance, calculate the surface area, and finally determine σ.

Answer 2

The surface charge density calculation is dependent on the surface area of the sphere, which can be obtained if the radius is provided. Without the radius, the exact surface charge density cannot be calculated.

Step-by-step explanation:

To calculate the surface charge density (σ) when given the potential on the surface of a sphere (V) and its capacitance (C), we use the relationship between capacitance, charge (Q), and potential: C = Q/V. From this, we can solve for Q: Q = C × V. Once we have Q, the surface charge density can be calculated using the formula σ = Q / A, where A is the surface area of the sphere.

Unfortunately, the question seems to be missing some details about the dimensions of the sphere, so we cannot proceed with calculating the exact surface charge density without that crucial piece of information.

If we had the radius of the sphere, we could calculate its surface area using A = 4πr² and then divide the total charge by this area to get σ in coulombs per square meter (σ = Q / (4πr²)). The result could then be converted to nanocoulombs per square meter (nC/m²) by multiplying by 10⁹.