E-field of solid sphere with non-uniform charge density

• mncyapntsi
In summary, the conversation is about a problem related to charge density and Gauss's law. The person is trying to solve the problem but is getting a different answer from the given solution. They ask for help and are advised to show their work and the given charge density. It is mentioned that the given solution is correct if the charge density is $\rho=ar^2$.
mncyapntsi
Homework Statement
Charge is distributed throughout a spherical volume of radius R with a density
where is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.
Relevant Equations
netEflux = qin/e0, and EA = qin/e0
Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below?

However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an error on my part, or if there is perhaps a type on the solutions?
Thanks a lot!

Your post is missing many relevant equations

And we can't tell where your mistakes, if any, are if you don't show us your work.

You got to tell us what is the given function of the charge density. I suspect that it is something that is spherically symmetrical. Generally when you write for a homework problem here in PF, it is of most importance to give the exact statement of the problem as it is given to you or written in the book you using.

Edit: Is the given charge density $$\rho=ar^2$$? If yes then the book solution is correct.

BUT as others have already said, you must show us your own solution if you want us to pinpoint your mistakes

Last edited:

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

The formula for calculating the electric field of a solid sphere with non-uniform charge density is E = (1/4πε0) * (Q/r2) * (1 - (r2/R2)), where ε0 is the permittivity of free space, Q is the total charge of the sphere, r is the distance from the center of the sphere, and R is the radius of the sphere.

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

The electric field of a solid sphere with non-uniform charge density is not constant throughout the sphere, unlike a sphere with uniform charge density. The electric field is strongest at the surface of the sphere and decreases as you move towards the center of the sphere.

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

Yes, the electric field of a solid sphere with non-uniform charge density can be negative. This occurs when the distance from the center of the sphere is greater than the radius of the sphere, resulting in a negative value for the electric field.

4. How does the electric field of a solid sphere with non-uniform charge density change as the distance from the center of the sphere increases?

The electric field of a solid sphere with non-uniform charge density decreases as the distance from the center of the sphere increases. This is because the charge density becomes more spread out as you move away from the center, resulting in a weaker electric field.

5. What is the significance of the non-uniform charge density in the electric field of a solid sphere?

The non-uniform charge density in the electric field of a solid sphere is significant because it allows for a more realistic representation of charged objects. In real-world situations, objects often have varying charge densities, and understanding the electric field of a solid sphere with non-uniform charge density can help in analyzing and predicting the behavior of these objects.

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