Electric Flux Comparison: Gauss's Theorem and Enclosed Charge

In summary, the conversation discusses two concentric imaginary spherical surfaces of different radii surrounding a point charge -Q at the center. The question is whether the electric flux through the two surfaces, I1 and I2, would be the same if calculated using different equations. The answer is that although the surface area and electric field at different distances would change, the overall result remains the same due to Gauss's Theorem and the equation I=q/ε. The conversation also touches on the relationship between electric field and distance, and the formula for electric field due to a point charge. It is concluded that the magnitude of the electric field is different at different distances, with a greater difference between R and 3R.
  • #1
VU2
35
0
Two concentric imaginary spherical surface of radius R and 3R, respectively, surrounds a point charge -Q, located at the center of the surface. When compared to the electric flux I1 through the surface of radius R, the electric flux I2 through the surface 3R is.

I know the answer is that I1=I2 based on Gauss's Theorem, I=q/ε, where q is the charge enclosed. But wouldn't the two flux's change if we instead use, I=E(dA), because of different radius in the dA portion? Can someone explain to me how will we get the same, I, if we use the latter equation? Thanks.
 
Physics news on Phys.org
  • #2
VU2 said:
Two concentric imaginary spherical surface of radius R and 3R, respectively, surrounds a point charge -Q, located at the center of the surface. When compared to the electric flux I1 through the surface of radius R, the electric flux I2 through the surface 3R is.

I know the answer is that I1=I2 based on Gauss's Theorem, I=q/ε, where q is the charge enclosed. But wouldn't the two flux's change if we instead use, I=E(dA), because of different radius in the dA portion? Can someone explain to me how will we get the same, I, if we use the latter equation? Thanks.

The surface area changes , but so does the electric field . The electric field at distance R and 3R are different .

Both surfaces give same result.
 
  • #3
Thanks Tanya for replying. But is the magnitude of E the same for both radius's?
 
  • #4
VU2 said:
But is the magnitude of E the same for both radius's?

What is the formula of electric field at distance 'x' due to a point charge ?
 
  • #5
E=kq/x^2
 
  • #6
Now for x = R and x=3R ,do you get same values of E or different ?
 
  • #7
So at the magnitude of the electric field is actually 4 times more for radius R than 2R?
 
  • #8
Im sorry, I meant 9 times more.
 
  • #9
Yeah, its much different. Thanks!
 

1. What is Gauss' theory?

Gauss' theory, also known as Gauss's law, is a fundamental principle in physics that describes the relationship between electric fields and electric charges. It states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space.

2. What is the significance of Gauss' theory?

Gauss' theory is significant because it provides a mathematical description of the behavior of electric fields and charges. It has been used to solve a wide range of problems in electromagnetism and has been fundamental in the development of technologies such as electric motors and generators.

3. How did Gauss develop his theory?

Gauss developed his theory through a series of experiments and mathematical calculations. He was able to observe the relationship between electric fields and charges and formulate his law through his understanding of mathematics and physics.

4. Can Gauss' theory be applied to all electric fields?

Yes, Gauss' theory can be applied to all electric fields. It is a fundamental principle that governs the behavior of electric fields and charges, and it has been extensively tested and proven to be valid in a variety of situations.

5. Are there any limitations to Gauss' theory?

While Gauss' theory is a powerful tool in understanding and predicting the behavior of electric fields, it does have some limitations. It assumes that the electric fields and charges are static and do not change over time. It also does not take into account the effects of relativity or quantum mechanics, which are important in extreme situations or at a very small scale.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
962
  • Introductory Physics Homework Help
Replies
2
Views
811
  • Introductory Physics Homework Help
Replies
17
Views
285
  • Introductory Physics Homework Help
Replies
2
Views
972
  • Introductory Physics Homework Help
Replies
11
Views
275
  • Introductory Physics Homework Help
Replies
26
Views
425
  • Introductory Physics Homework Help
Replies
3
Views
711
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
757
Back
Top