Final answer:
To calculate the surface charge density on the sphere, the surface area was first determined using the sphere's radius, and the provided charge was then divided by this area, yielding a charge density of approximately -3.60 x 10^-4 C/m^2.
Step-by-step explanation:
The problem provided can be solved using the concept of surface charge density, which in physics denotes the amount of electric charge per unit area. To find the charge density on the surface of the sphere, we need to use the formula for the surface area of a sphere and the given charge.
The formula for surface area (A) of a sphere is given by:
A = 4πr^2
Where r is the radius of the sphere. The diameter given is 16.0 cm, hence the radius is half of that: r = 8.0 cm = 0.08 m.
Now, we find the surface area:
A = 4π(0.08 m)^2 = 4π(0.0064 m^2) = 0.0256π m^2
To find the charge density (σ), we use the formula:
σ = charge / surface area
Converting -29.0 μC to coulombs (μC to C) gives us -29.0 × 10^-6 C. Now we can calculate the charge density:
σ = (-29.0 × 10^-6 C) / (0.0256π m^2)
σ = -29.0π10^-6 C / 0.0804 m^2
σ ≈ -3.60 × 10^-4 C/m^2
The negative sign indicates that the charge is negative, as in the case of electrons. Thus, the surface charge density is approximately -3.60 × 10^-4 C/m^2.