How Is Electric Flux Calculated for a Charged Sphere?

[22steve]

Homework Statement

A uniformly charged conducting sphere of 1.6 m diameter has a surface charge density of 8.0 µC/m2. What is the net charge of the sphere, and what is the total electric flux leaving the surface of the sphere?

Homework Equations

surface charge density = q/A
flux = E x A
flux = charge enclosed/ permittivity constant (Epsilon-naught)

The Attempt at a Solution

q = surface charge density x A
so (8e-12)x(4xpix 0.8^2) = 6.434e-11
then E = k(q/r^2) = .90377 = E
so flux = E x A = .90377x 4x pi x .8^2

 

[Doc Al]

The Attempt at a Solution

q = surface charge density x A
so (8e-12)x(4xpix 0.8^2) = 6.434e-11

Careful: μC = 10^-6C.

then E = k(q/r^2) = .90377 = E
so flux = E x A = .90377x 4x pi x .8^2

That's too much work. Once you find the correct charge, just use Gauss's law to find the flux. (But your method would work also. )

 

[nlightner]

= 2.293e-10

I would like to verify the given information and equations used to solve this problem. The surface charge density, q, is defined as the charge per unit area, where q is the total charge and A is the area. In this case, q is given as 8.0 µC/m2 and the area of the sphere is calculated using its diameter as 1.6 m. The resulting value for q is 6.434e-11 C.

Next, the electric field, E, can be calculated using Coulomb's law, where k is the Coulomb constant, q is the total charge, and r is the distance from the center of the sphere. Using the given information, the value of E is calculated to be 0.90377 N/C.

Finally, the electric flux is given by the product of the electric field and the area, which is 2.293e-10 Nm2/C.

To find the net charge of the sphere, we can use the equation for electric flux as flux = q/ε0, where ε0 is the permittivity constant. Rearranging this equation, we get q = ε0 x flux. Using the calculated value for flux and the known value for ε0, the net charge of the sphere is found to be 1.829e-10 C.

In conclusion, the net charge of the sphere is 1.829e-10 C and the total electric flux leaving the surface of the sphere is 2.293e-10 Nm2/C. It is important to note that these values may vary depending on the accuracy of the given information and the equations used. Further experimentation and verification may be necessary to confirm these values.