A uniformly charged conducting sphere of 1.3 m diameter has a surface charge density of 8.7 µC/m2. (a) Find the net charge in coulombs on the sphere. (b) What is the total electric flux leaving the surface of the sphere?
To find the net charge on the conducting sphere, you need to calculate the total charge on the surface of the sphere.
To do this, you can use the formula:
Charge = Surface Area × Surface Charge Density.
Where Charge is the net charge on the sphere, Surface Area is the surface area of the sphere, and Surface Charge Density is the given value of 8.7 µC/m^2.
(a) Let's start by calculating the surface area of the sphere using the formula:
Surface Area = 4πr^2
Since the diameter of the sphere is given as 1.3 meters and the radius (r) is half the diameter, we have:
r = 1.3 m / 2 = 0.65 m.
Now, calculate the surface area:
Surface Area = 4π(0.65 m)^2.
Calculate the value and keep it for further use.
(b) To find the total electric flux leaving the surface of the sphere, you can use Gauss's law. According to Gauss's law, the electric flux through a closed surface is directly proportional to the total charge enclosed by the surface.
The electric flux (Φ) is given by the equation:
Φ = q / ε₀,
Where q is the total charge enclosed by the surface and ε₀ is the permittivity of free space.
In this case, the sphere is a conducting sphere, which means the net charge resides on the surface. Therefore, the total charge (q) is equal to the net charge on the sphere.
Now, you need to calculate the electric flux using the given surface charge density. The surface charge density (σ) is related to the total charge (q) by the formula:
σ = q / (4πr^2),
Where r is the radius of the sphere.
Rearranging the equation, we can solve for q:
q = σ × 4πr^2.
Substitute the value of σ and r from your calculations and solve for the net charge (q).
(c) Now that you have the net charge (q), you can use it to find the total electric flux (Φ) by using the equation Φ = q / ε₀.
Substitute the value of q and the value of the constant ε₀ (8.854 × 10^-12 C^2/N·m^2), and calculate the total electric flux leaving the surface of the sphere.
Some of us have tried everything (book and looking at notes), and still can't figure it out.>:(
A formula and some pointers would really help, instead of asking some judgement questions!