Electric Flux and Net Charge

In summary, we can calculate the net charge of a uniformly charged conducting sphere with a 1.6 m diameter and a surface charge density of 8.0 µC/m2 by using the equation q = surface charge density x A. By substituting the given values, we get a net charge of 6.434e-11 C. To find the total electric flux leaving the surface of the sphere, we can use Gauss's law, which states that flux is equal to the enclosed charge divided by the permittivity constant. By using the calculated net charge and the given values, we get a flux of 3.989e-11 Nm2/C.
  • #1
12
0

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
 
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  • #2
22steve said:

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. :wink:)
 
  • #3
= 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.
 

1. What is electric flux?

Electric flux is a measure of the amount of electric field passing through a given area. It is calculated by multiplying the strength of the electric field by the area it passes through at a right angle.

2. How is electric flux related to net charge?

The electric flux passing through a closed surface is directly proportional to the amount of net charge enclosed by that surface. This is known as Gauss's law.

3. What is net charge?

Net charge is the sum of all positive and negative charges in a given system. It can be calculated by adding up the individual charges present.

4. How is electric flux affected by the shape of a surface?

The electric flux passing through a surface depends on the orientation and shape of the surface relative to the electric field lines. A larger surface area or a surface perpendicular to the field lines will result in a higher electric flux.

5. Can electric flux be negative?

Yes, electric flux can be negative. This occurs when the electric field and the surface are in opposite directions, resulting in a negative product. However, the absolute value of electric flux is always positive.

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