Electric field and gauss law for different models of sphere

[exuberant.me]

Hello all! I actually have a few doubts regarding "gauss law" when applied "for different models of sphere"

First, If we place a charge 'Q' inside a spherical shell at the center (somehow) then it should come out to its surface that means in no way can we do it. True or False?

Next,

Considering a solid sphere having a charge Q uniformly distributed on its outer surface. Thus everywhere inside it is the electric field equal to 0.

But i have somewhere read that the electric field inside a solid sphere is Kqr/R^3.

Or is it that , there is a difference in these two statements
"A charge uniformly distributed on the surface of a solid sphere" and
"A symmetrical spherical distribution of charge" ?

Also, How can we get a spherical symmetrical distribution of charge?
. By placing the charge at the center of the solid sphere? (which is again impossible i guess)

I'll be greatly thankful if someone clears these brain storming doubts?

 

[tiny-tim]

hello exuberant.me!

(try using the X² button just above the Reply box )

First, If we place a charge 'Q' inside a spherical shell at the center (somehow) then it should come out to its surface that means in no way can we do it. True or False?

sorry, no idea what you mean

But i have somewhere read that the electric field inside a solid sphere is Kqr/R^3.

Or is it that , there is a difference in these two statements
"A charge uniformly distributed on the surface of a solid sphere" and
"A symmetrical spherical distribution of charge" ?

yes … Kqr/R³ is for a charge uniformly distributed throughout the volume (use gauss law! )

Also, How can we get a spherical symmetrical distribution of charge?
. By placing the charge at the center of the solid sphere? (which is again impossible i guess

no, by chucking the charges in, and giving them a good old stir …

like making a pudding ​

 

[jtbell]

like making a pudding ​

With no lumps, of course... nice and smooth...

 

[BruceW]

Also, How can we get a spherical symmetrical distribution of charge?

mathematically,
$$\frac{\partial \rho}{\partial \theta} = \frac{\partial \rho}{\partial \phi} = 0$$
and practically how this could happen for a solid sphere with fixed charges? ...err... maybe in Neutron stars that have a surplus of electrons? The electrons wouldn't be fixed, but in equilibrium the charge distribution would be spherically symmetric... unless it was a pulsar?

So you just have to make a neutron star :) easy-peasy.

 

[sardar]

Hello there! These are great questions about electric field and gauss law for different models of spheres. Let me try to address them one by one.

First, regarding the placement of a charge inside a spherical shell, it is true that the charge will distribute itself evenly on the surface of the shell due to the repulsion of like charges. This is known as the "shell theorem" and is a consequence of gauss law. So in that sense, it is not possible to have a charge placed inside a spherical shell without it coming out to the surface.

Next, you are correct in stating that the electric field inside a solid sphere with a uniform charge distribution is zero. This is because the electric field due to each small element of charge inside the sphere cancels out with the electric field due to another element in the opposite direction, resulting in a net zero field inside the sphere. However, the formula you mentioned, Kqr/R^3, is for the electric field outside of a solid sphere, where 'r' is the distance from the center of the sphere. This formula is derived using gauss law and takes into account the total charge of the sphere and the distance from the center.

The difference between a charge uniformly distributed on the surface of a solid sphere and a symmetrical spherical distribution of charge is that the latter refers to any spherical distribution of charge, not necessarily a uniform one. This can be achieved by placing the charges at specific points on the surface of the sphere, rather than uniformly distributing them.

Lastly, a spherical symmetrical distribution of charge can be achieved by placing the charge at the center of the sphere, as long as the charge is evenly distributed on the surface of the sphere. This is possible in theory, but practically it is difficult to achieve as it would require precise placement of each charge.

I hope this helps to clear up your doubts. Keep exploring and asking questions, that's what science is all about!