A spherical conducting shell in an electric field field

[transparent]

If a spherical conducting shell is kept in an electric field (say, from a point charge kept at some distance outside the shell), will any charge be induced in the internal surface of the shell? Also what will the field be like inside the shell? Thanks.

 

[Jano L.]

If the interior of hte sphere does not contain free charge (usually the case if we did not put it there intentionally), the outer metallic shell of the sphere will shield the external field, so that in the metal and inside the sphere there is zero net field.

 

[transparent]

If the interior of hte sphere does not contain free charge (usually the case if we did not put it there intentionally), the outer metallic shell of the sphere will shield the external field, so that in the metal and inside the sphere there is zero net field.

Thanks. What about the charge? Will there be any charge on the inner surface of the shell? Also, how does the shielding effect work?

 

[Jano L.]

No. The shielding works this way: in static situation, there cannot be no currents in the metal, so electric field in the metal has to vanish. Due to Gauss' law, this also means there is zero charge density throughout the metal of the sphere. The only non-zero charge density can be at the surface and will be distributed in such a way so that it can completely cancel the external field.

 

[sardar]

I can provide an explanation for the behavior of a spherical conducting shell in an electric field.

Firstly, the conducting shell acts as a Faraday cage, which means it can shield the inside from external electric fields. This is because the charges on the surface of the shell will rearrange themselves in such a way that the electric field inside the shell is zero. This is known as the principle of superposition, where the total electric field is the sum of the external field and the field created by the induced charges on the surface of the shell.

Now, to answer the first question, yes, there will be an induced charge on the internal surface of the shell. This is because the electric field from the external point charge will polarize the conducting shell, causing opposite charges to accumulate on the inner surface. This induced charge will create its own electric field, which will cancel out the external field inside the shell.

As for the field inside the shell, it will be zero due to the principle of superposition. This means that any charges placed inside the shell will not experience any force from the external electric field. However, if there are other charges inside the shell, they will create their own electric field, which will not be affected by the external field.

In summary, a spherical conducting shell in an electric field will have an induced charge on the internal surface and the field inside the shell will be zero due to the principle of superposition. This behavior is important in many applications, such as in electronic devices and electromagnetic shielding.