Question

why it is a property of hollow conducting any random body to give net electric field inside as zero ,(the charge distribution is not uniform but even then the net field is zero inside)why that bizarre arrangement is made by the nature
in short why hollow metal bodies give Faraday caging

Answer 1

Consider that the conducting shell is made of relatively still, positively charged protons with a sea of negatively charged electrons that can flow anywhere. Since like charges repel, they are going to push themselves to the edge of the object to repel from the other electrons inside the conductor.

Answer 2

This property of a hollow sphere is due to Gauss's Law.

\[\Phi _{E}=\int\limits_{a}^{b}E*dA\] where the path from a to b forms a closed path.

If you pick a spherical surface area that fits inside the hollow sphere and evaluate Gauss's Law then:

\[\phi _{E}=\int\limits_{a}^{b}\frac{ k _{e}*q }{ r^2 }*dA=\frac{ k _{e}*q }{ r^2 }*\int\limits_{a}^{b}dA\]

Now the integral is simply equal to the surface area of a sphere.

\[\int\limits_{a}^{b}dA=A _{sphere}=4*\pi*r^2\]

\[\phi _{E}=\frac{ k _{e}*q }{ r ^2}*4*\pi*r^2=4\pi*k _{e}*q\]

\[k=\frac{ 1 }{ 4\pi*\epsilon }\]

\[\phi _{e}=\frac{ q }{ \epsilon }\]

Now you have the equation for the net electric flux through a spherical surface inside your metal sphere. Notice the equation requires the total charge held within this arbitrary surface. All of the charge is on the hollow metal sphere and no charge exists within. Therefore, the net flux through the middle of the sphere is zero. Gauss's Law goes on to state that the net electric flux through an arbitrary surface is equal to total charge within divided by the permittivity, as seen in the previous equation.

Answer 3

hey the above derivation is also valid for non conducting hollow bodies which have some charge then why it is not true for them
further can u xplain it with the help of physics

Answer 4

further i am asking about an arbitrary metal surface and not of hollow sphere

Answer 5

Ok, I believe that I understand what you're asking for. The previous derivation was for Gauss' Law which is a conservation law. It basically says that "what goes into a volume is equal to what comes out if there's no charge present", hence a zero net flux. If a charge is present, then the "net" electric flux is proportional to the charge within. This is true regardless whether you use a conductor or insulator. Careful, don't confuse electric flux with electric field.

For a conductor, the charges will position themselves evenly and symmetrically from each other. Now ask yourself, is there a potential difference between a point charge and its symmetric counterpart on the other side of the sphere? No, electric fields do not flow from one negative charge to another. Essentially, the charges' electric fields cancel within the sphere. Another example: What is the potential difference between two 12V batteries? 0V, because they are both at 12V. This is why there is no electric field within a hollow conducting sphere.

For an insulator, the charges cannot redistribute themselves so there will be an unbalanced surface charge density on the sphere. This imbalance leads to non-symmetric electric fields which can cause an electric field to exist in the center of the sphere. However, the net electric flux (density of electric field lines per area) will still be zero (assuming no charge in the center).

Answer 6

talk about an arbitrary metal body like paint-can etc they too give electrostatic shielding
further why that bizarre charge distribution that give field inside as zero