If there is a point charge inside a shell conductor for example, making a Gaussian surface around the point charge will tell me there is a non-zero flux, meaning non-zero electric field inside, but how is that possible if electric field inside any conductor is zero because charges on the inner surface redistribute to cancel the electric field?
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1$\begingroup$ But that point charge is in the cavity, so what's the problem in having an electric field inside the cavity? $\endgroup$– user258881Commented May 9, 2020 at 5:29
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4 Answers
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Metals have access to a sea of free electrons. Under equilibrium condition the net movement of the electrons inside the metal is zero. And this is reflected in the fact that metals have no field inside them.
To answer your comment:
Why doesn't the point charge in the cavity induce a charge distribution on the inner surface of the conductor that will cancel the field inside?
Simply because the charge distribution at the inner surface is such that the field in the metal is zero. This need not balance the field in the cavity.
answered May 9, 2020 at 7:33
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When we say that the net electric field inside a conductor is zero, what we mean precisely is that it is zero inside the meat of the conductor. When you put the point charge inside, the electric field was precisely zero between the inner and outer surface of the conductor. The inside part(where the charge is present) is not the meat of the conductor.
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$\begingroup$ Why doesn't the point charge in the cavity induce a charge distribution on the inner surface of the conductor that will cancel the field inside? $\endgroup$– DarkeninCommented May 9, 2020 at 5:57
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$\begingroup$ Simple answer- Because it can not. There is no reason why it would be able to do so. For every arbitrary gaussian surface you draw inside the cavity, the net charge inside would be $q$ since there can be no inductions in free space. So, since $$\displaystyle \int \textbf{E}.\textbf{ds} \neq 0$$ for any arbitrary surface, electric field has to be non zero any way. $\endgroup$– PhysikerCommented May 10, 2020 at 3:42
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The electric field inside a conductor is zero in a static situation. Static means, when the charges are in rest. When there's an electric field inside a conductor, the free electrons will move until the electric force (and thus the electric field) acting on them becomes zero.
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You are giving 2 situations in 1st case when there is a sphere with uniform charge density there must be charge inside the gaussian surface which means there must be an electric field CASE 2 In case I of conductors the charge electric field inside the conductor has to be 0 so all charge in a conductor resides on the surface . The charge enclosed in the gaussian surface conductor becomes 0