Why dont integrate all electric fields in a sphere?

In summary, integrating electric fields in a sphere is important for understanding and analyzing the overall electric field in a given region, especially when the field is changing or varying. While electric fields can be integrated in other shapes, a sphere is often preferred due to its simplicity and uniform distribution of electric fields. The integration process in a sphere is different from other shapes because the field strength is the same at any point on the surface and decreases predictably as you move away from the center. Additionally, integrating electric fields in a sphere can be used to calculate the electric potential, which has many real-world applications such as in the design of electric circuits, studying charged particles, and industries like telecommunications and energy production.
  • #1
axcelenator
33
0
If volumetric charge distribution has spherical symmetry
I want to find the trapped charge a in certain radius
Why did not need to do an integral from 0 to R to all the electric fields inside the sphere but take only the external field(how gauss law says)?

The Electric fiels is: E=3AB*r*e^(-1.5Br^2)
 
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  • #2
You could do that, it's just that the result for the field inside the radius is zero.
 

1. Why is it important to integrate electric fields in a sphere?

Integrating electric fields in a sphere is important because it allows us to understand and analyze the overall electric field within a given region. This is especially useful in situations where the electric field is changing or varying in strength.

2. Can electric fields be integrated in any shape other than a sphere?

Yes, electric fields can be integrated in any shape as long as the shape is symmetrical and the electric field is uniform throughout the region. However, integrating in a sphere is often preferred due to its simplicity and ease of calculation.

3. How is the integration of electric fields in a sphere different from other shapes?

The integration of electric fields in a sphere is different from other shapes because a sphere has a uniform distribution of electric fields. This means that the electric field strength is the same at any point on the surface of the sphere and it decreases in a predictable manner as you move away from the center.

4. Can the integration of electric fields in a sphere be used to calculate the electric potential?

Yes, the integration of electric fields in a sphere can be used to calculate the electric potential. This is because the electric potential is directly related to the electric field, and integrating the electric field over a sphere allows us to calculate the total potential within that sphere.

5. What are some real-world applications of integrating electric fields in a sphere?

The integration of electric fields in a sphere has many practical applications, such as in the design of electric circuits, the calculation of the electric field in a charged particle, and the study of the Earth's magnetic field. It is also used in industries such as telecommunications, electronics, and energy production.

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