Calculating the flux through the spherical surfaces at certain radius

In summary, a person is asking for confirmation of their answer to a problem involving calculating flux through spherical surfaces. They ask for clarification on the units for flux and the use of a vector in the solution. The expert suggests a simpler method using a formula and unit vector.
  • #1
falyusuf
35
3
Homework Statement
Point charges 5 uC, -3 uC, 2 uC and 10 uC are located at (-12, 0,5). (0, 3,-4),(2, -6, 3) and (3, 0, 0), respectively. Calculate the flux through the spherical surfaces at:
i) r= 1
ii) r= 10
iii) r=15

* u = 10^-6 *
Relevant Equations
Attached below.
Relevant Equation:
1637442267037.png

My attempt:
1637444699332.png

1637444677296.png

Could someone please confirm my answer?
 

Attachments

  • 1637444649520.png
    1637444649520.png
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  • #2
You can't magically greate 10 digit accuracy results from 1 digit givens !

What is ##Q_{enc}## for ##r= 1## ?

##\ ##
 
  • #3
BvU said:
You can't magically greate 10 digit accuracy results from 1 digit givens !

What is ##Q_{enc}## for ##r= 1## ?

##\ ##
Yes the answers I got were not reasonable and tried to figure out my mistakes but I couldn't.

I think it's -3 uC as r in the point (0, 3,-4) is 0, which is less than r=1.
so, the total charge enclosed is -3 uC.
 
  • #4
I must asssume you have correctly given the problem statement
Calculate the flux through the spherical surfaces at:
i) r= 1
etc. And my interpretation is that such spheres are centered at the origin. So that the enclosed charge is zero for ##r=1##.
And that you are making a fairly simple exercise quite complicated unnecessarily.

Like in the other problem: what are the units for flux in your textbook ?

##\ ##
 
  • #5
BvU said:
Like in the other problem: what are the units for flux in your textbook ?
It's Coulomb.

1637580341128-png.png
 
  • #6
BvU said:
And my interpretation is that such spheres are centered at the origin. So that the enclosed charge is zero for r=1.
Sorry, I didn't get it. Could you explain further?
 
  • #7
falyusuf said:
It's Coulomb.

View attachment 292834
Confusing (for me, at least). SI unit for electric flux is different.

falyusuf said:
Sorry, I didn't get it. Could you explain further?
The exercise asks for the flux through a spherical shell with radius 1 around the origin (then 10, then 15).

I don't understand what you do with your ##\overline{R_1}## etc.

* u = 10^-6 *
There is a ##\mu## under the 'insert symbol' button:
1637581967289.png


But (much better): with a little ##\LaTeX## you can do all kinds of math. ##\mu## becomes ##\mu##

There is a guide button at lower left:

1637582094065.png


##\ ##
 
  • #8
BvU said:
I don't understand what you do with your R1― etc.
I assume that R1 is the vector between point 1 and the origin and found it by
1637583076411.png
 
  • #9
What would you need that vector for ?

##\ ##
 
  • #10
BvU said:
What would you need that vector for ?

##\ ##
Get its length and substitute it in this formula:
1637584144098.png
 
  • #11
1637586213881.png

Seems to me ##\overline {a_R}## is a unit vector. Right ?

This formula calculates ##\overline D## at the origin. Not what you want. The exercise asks for a flux (in your case apparently an electric displacement flux).

##\ ##
 
  • #12
BvU said:
Seems to me aR― is a unit vector. Right ?
BvU said:
Seems to me aR― is a unit vector. Right ?
Yes. I think about it more and find that it'll be easier to get r from the given points using this formula:
1637589969545.png

and then simply;
1637595565755.png

Right?
 
  • #13
Makes much more sense to me than post #1 !
And no hassle with 10-digit numbers either :wink:

##\ ##
 
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  • #14
BvU said:
Makes much more sense to me than post #1 !
And no hassle with 10-digit numbers either :wink:

##\ ##
Thank you so much. Appreciate your help
 
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Likes BvU

1. What is flux and why is it important to calculate it through spherical surfaces?

Flux is the measure of the flow of a physical quantity through a given surface. In the context of spherical surfaces, it represents the amount of a physical quantity passing through a spherical surface at a certain radius. Calculating flux through spherical surfaces is important in various fields of science, such as physics and engineering, as it helps in understanding the flow of energy or matter in a given system.

2. How is the flux through spherical surfaces at a certain radius calculated?

The flux through a spherical surface at a certain radius can be calculated using the formula: Φ = E * A * cosθ, where Φ is the flux, E is the magnitude of the electric field, A is the area of the spherical surface, and θ is the angle between the electric field and the normal vector of the surface.

3. Can the flux through spherical surfaces at different radii be calculated using the same formula?

No, the formula for calculating flux through spherical surfaces at a certain radius only applies to a specific radius. If the radius changes, the area of the surface and the angle between the electric field and the normal vector will also change, thus requiring a different formula to calculate the flux.

4. What are some real-world applications of calculating flux through spherical surfaces?

Calculating flux through spherical surfaces has various real-world applications, such as in understanding the flow of heat in a spherical object, analyzing the electric field around a charged spherical object, and studying the radiation emitted by a spherical source.

5. Are there any limitations to calculating flux through spherical surfaces at certain radii?

Yes, there are limitations to calculating flux through spherical surfaces at certain radii. The formula used to calculate flux assumes that the electric field is constant over the entire surface, which may not always be the case in real-world scenarios. Additionally, the shape of the spherical surface may also affect the accuracy of the calculated flux.

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