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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
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?
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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