Why Do Solid and Hollow Spheres Show Different Electric Fields Inside?

In summary, The first example involves an insulating solid sphere with a uniform volume charge density and the second example involves a thin spherical shell with a uniform surface charge density. The field inside a hollow spherical shell is zero, but not outside, as the first example shows. If a solid sphere is thought of as an infinite series of shells, the shells farther inside would contribute to the field at a given point. It is important to understand gauss' law in order to fully comprehend these examples.
  • #1
Acuben
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As I was studying gauss's law to understand it's concept (which I still do not understand)
I came across two similar (or same?) looking problems that seems to give different result

Homework Statement


example 1)
An insulating solid sphere of radius a has a uniform volume charge density (rho) and carries a total positive charge Q
a) find magnitude of E at a point outside the sphere
b) find magnitude of E at a point inside the sphere
answer a) E=kQ/r^2
answer b)kQr/a^3
note: textbook used Qin=(rho)*(V')
and EA=Qin/e
where e is permititvity of vacuum or something >_>
r is for radius of the gaussian sphere

example 2)
A thin spherical shell of radius a has a total charge Q distributed uniformly over its surface. Find Electric field at points
a) outside
b) inside
answer a) E=kQ/r^2
answer b) E=0
note: not much work shown here

These are examples problems meaning all the work is shown on the textbook
example 1a sounds logical since E=kQ/r^2 is the equation of Electric field.
Even it is on gaussian sphere, it wouldn't make a difference which is same for example 2a.
Now for example 1b and 2b, why is it that two examples that seems to be the same problems
(both involving sphere). gives two different E (while they are both spheres of radius r and charge Q
distributed uniformly)It did say say example 1 is insulating solid sphere. I'm thinking maybe this is the reason.
In insulating sphere where charge is spread out, there are charges inside the shell, not just on the outside. (although what I still do not understand is that solid sphere should still have E=0 since hollow spherical shell have E=0, and solid sphere can be viewed as sum of thin hollow spherical shell (if you consider thin hollow spherical shell as dA but Integral of dA would be 0 since dA is 0... >_> I think I'm wrong but I do not know why.)
and example 2 is thin spherical shell. Does this make a difference?
or do I count first one as filled in sphere and 2nd one as hollow sphere?

Homework Equations


The Attempt at a Solution

 
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  • #2
Acuben said:
In insulating sphere where charge is spread out, there are charges inside the shell, not just on the outside. (although what I still do not understand is that solid sphere should still have E=0 since hollow spherical shell have E=0, and solid sphere can be viewed as sum of thin hollow spherical shell (if you consider thin hollow spherical shell as dA but Integral of dA would be 0 since dA is 0... >_> I think I'm wrong but I do not know why.)
The field inside a hollow spherical shell is zero, but not outside, as the first example shows. If you think of a solid sphere as an infinite series of shells (which is totally fine), the shells outside would contribute nothing to the field (as you say); but the shells farther inside would contribute to the field at a given point.

You should work on understanding gauss' law. Is there something in particular that doesn't make sense?
 
  • #3
that makes sense, thank you =>
 

FAQ: Why Do Solid and Hollow Spheres Show Different Electric Fields Inside?

What is the equation for the electric field of a sphere?

The equation for the electric field of a sphere is given by E = kQ/r^2, where k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere to the point where the electric field is being measured.

How does the electric field of a sphere vary with distance?

The electric field of a sphere follows an inverse square relationship with distance, meaning that as the distance from the center of the sphere increases, the electric field strength decreases.

What is the direction of the electric field of a sphere?

The direction of the electric field of a sphere is always radially outward, meaning that it points away from the center of the sphere.

How does the charge of a sphere affect its electric field?

The electric field of a sphere is directly proportional to the charge of the sphere. This means that as the charge of the sphere increases, the electric field strength also increases.

Can the electric field of a sphere be negative?

Yes, the electric field of a sphere can be negative if the charge of the sphere is negative. The negative sign in the equation for the electric field indicates the direction of the field, not the magnitude.

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