# Electric Field of a solid sphere of non-uniform surface density

• vtv
In summary, the conversation is discussing the surface charge density of a solid sphere, represented as Rho(r). It is specified that for the region 0 < r < a, the value is equal to k1, and for the region a < r < R, the value is equal to k2. The question at hand is to find the electric field in each of the three regions of the sphere (r < a, a < r < R, and R < r). The attempted solution is attached, but the mentor suggests typing it out and providing more thorough explanation for each step. The mentor also notes that k2 x ( a < r < R) may be a typo and should perhaps be just k2 or k2r
vtv
A solid sphere has surface charge density, Rho (r)

Rho(r) = k 1 ( 0 < r < a)

k2 x ( a < r < R)

2)
Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R <
The attempted solution and the question with the diagram is attached below

Could the answer be verified particularly for region 2 ?!

<< Mentor Note -- fixing up picture some... >>

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What you describe is not a surface charge density. It is just a charge density.

Even with the mentors cleaning up your image it is difficult to read (and impossible to quote). I suggest that you type it out and explicitly flesh out your argumentation for each step.

vtv said:
k2 x ( a < r < R)
What does this mean? Should it be just k2, or perhaps k2r?

## 1. What is the formula for calculating the electric field of a solid sphere of non-uniform surface density?

The formula for calculating the electric field of a solid sphere of non-uniform surface density is E = (1/4πε0) * (Q/r2) * (1 + (3/2) * (a/b) * (r/R) 2), where Q is the total charge of the sphere, r is the distance from the center of the sphere, a is the non-uniform surface density at the surface of the sphere, b is the average surface density of the sphere, and R is the radius of the sphere.

## 2. How does the electric field of a solid sphere of non-uniform surface density differ from that of a uniform surface density?

The electric field of a solid sphere with non-uniform surface density is not constant throughout the sphere like a sphere with uniform surface density. It is stronger at the regions with higher surface density and weaker at regions with lower surface density. This is because the electric field is directly proportional to the surface density at a given point.

## 3. Can the electric field of a solid sphere of non-uniform surface density be negative?

Yes, the electric field of a solid sphere of non-uniform surface density can be negative. This occurs when the surface density at a certain point is negative, which means there is a net negative charge at that point. The electric field would then point towards the center of the sphere, opposite to the direction of a positive electric field.

## 4. How does the distance from the center of the sphere affect the electric field of a solid sphere of non-uniform surface density?

The electric field of a solid sphere of non-uniform surface density is inversely proportional to the square of the distance from the center of the sphere. This means that as the distance from the center increases, the electric field decreases. However, the electric field can be affected by the non-uniform surface density at the surface of the sphere, so the relationship may not be a perfect inverse.

## 5. What is the significance of the radius of the sphere in calculating the electric field of a solid sphere of non-uniform surface density?

The radius of the sphere is an important factor in calculating the electric field of a solid sphere of non-uniform surface density because it affects the strength of the electric field. As the radius increases, the electric field decreases due to the inverse square relationship. Additionally, the ratio of the radius to the distance from the center (r/R) also affects the electric field, with a larger ratio resulting in a stronger electric field.

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