Charge staggered over spherical volume.

In summary, the problem involves a charge placed in a volume of a sphere with a changing density. The task is to determine the potential at point A(0,0,0) with respect to a reference point at infinity using Gaussian law. The solution involves separating the potential into two parts and using different expressions for the electric field depending on the distance from the origin. The final expression for the potential is obtained by combining the two parts. The approach used is correct for solving similar problems involving potential.
  • #1
cdummie
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Homework Statement


There is charge placed in a volume of a sphere, whose density changes by expression ρ(r)=ρ0a/r for 0<r≤a and ρ(0)=0. Where a and ρ0 are known variables , and r is a distance from the origin. Determine the potential of the point A(0,0,0) with regard to reference point at infinity.

Homework Equations


Gaussian law.

The Attempt at a Solution


I solved it this way:

I separated potential into two parts like this:
формула за потенцијал у задатку.png

since there is different expression for changing of electric field at arbitrary point whose distance from origin is less than a, than for those whose distance is greater than a.

For finding E i used Gaussian law,
and this is what i got for E1:

лијева страна.png

десна страна.png
прво поље.png


Doing the same thing for the r greater than a, i got expression for E2 (difference is that i had different limits of integration when finding charge , it was from 0 to a instead of r since i took all of the charge there is):
друго поље.png

Placing it into first expression i got:

укупни потенцијал.png


Now my question is, is this correct, i mean is this correct approach for finding potential in examples like this?
 
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Everything looks good!
 
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Related to Charge staggered over spherical volume.

1. What does "charge staggered over spherical volume" mean?

"Charge staggered over spherical volume" refers to the distribution of electric charge in a spherical shape, where the charges are not evenly spread out but rather arranged in a staggered or offset pattern.

2. How is charge staggered over spherical volume different from a uniform distribution of charge?

In a uniform distribution of charge, the charges are evenly spread out over the entire spherical volume. In contrast, a staggered distribution means that the charges are arranged in a non-uniform or uneven manner, with some areas having higher concentrations of charge than others.

3. What causes charge to be staggered over a spherical volume?

The charge staggered over a spherical volume can be caused by various factors, such as the presence of other charges, the shape of the object, or external electric fields. It can also occur naturally in some materials due to their atomic or molecular structure.

4. What are the potential effects of a staggered charge distribution?

The effects of a staggered charge distribution can vary depending on the situation. In some cases, it may result in a stronger or weaker electric field in certain areas, which can affect the movement of charged particles. It can also contribute to the overall stability or instability of the object or material.

5. How is charge staggered over spherical volume relevant in scientific research?

Charge staggered over spherical volume is a common phenomenon that can be observed in various natural and artificial systems. Understanding its effects and behavior can help scientists in fields such as physics, chemistry, and materials science to better understand and manipulate electric charge in different environments.

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