Calculating Flux for Hemispheres of Different Radii

• Seraph404
In summary, the conversation discusses a scenario involving two hemispherical surfaces, a point charge, and an annular ring. The goal is to find the electric flux through these surfaces. The conversation also mentions the formula for electric flux and the attempt at solving the problem independently.
Seraph404

Homework Statement

For some reason, I'm not quite understanding this scenario.

"

Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position $$\vec{r}$$ due to the point charge is:

$$\vec{E}$$($$\vec{r}$$)= [C/(r^2)]*$$\hat{r}$$

where C is a constant proportional to the charge, r=|$$\vec{r}$$|, and $$\hat{r}$$=$$\vec{r}$$/r is the unit vector in the radial direction. "

I'm supposed to find electric flux through the three different surfaces, but for some reason, this picture just doesn't make sense to me.

Homework Equations

Electric flux is the integral of the dot product of electric field and dA (differential area element).

The Attempt at a Solution

I want to try figuring it out on my own first before I ask for help, but I don't quite understand this scenario. For example, I don't understand how the two images provided correlate, and I don't understand what the three different surfaces are. Sorry if the answer to this is obvious. ><

See attached file

Attachments

• flyingsaucer.jpg
16.4 KB · Views: 1,077
How do I open it?

You don't need to open it. It's just an image to help you understand the surfaces.

1. What is flux and why is it important?

Flux is a measure of the flow of a physical quantity through a given surface. It is important because it helps us understand how certain physical phenomena, such as heat or light, move through different objects or materials.

2. How is flux calculated for hemispheres of different radii?

The formula for calculating flux for hemispheres of different radii is F = E * A * cos(theta), where F is the flux, E is the electric field, A is the area of the hemisphere, and theta is the angle between the electric field and the normal to the surface.

3. What factors can affect the flux calculation for hemispheres of different radii?

The factors that can affect the flux calculation include the radius of the hemispheres, the electric field strength, and the angle between the electric field and the normal to the surface. Other factors may also include the material of the hemispheres and the distance between them.

4. Can flux be negative for hemispheres of different radii?

Yes, flux can be negative for hemispheres of different radii. This means that the flow of the physical quantity, such as electric field or heat, is in the opposite direction of the surface normal. It is important to consider the direction of the physical quantity when calculating flux.

5. How can calculating flux for hemispheres of different radii be applied in real-life situations?

Calculating flux for hemispheres of different radii can be applied in various real-life situations, such as in electrical engineering to determine the flow of electric fields through different materials, or in meteorology to understand the flow of heat or air through different surfaces. It can also be used in physics experiments and simulations to study the behavior of physical quantities in different scenarios.

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