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I have a few related questions about static electricity and conductors. 1. when we say static electric field inside a conductor is zero, let us take an example of two concentric conductors, outer one positively charged and inner negative charged -- inside inner sphere field will be zero, but there will be field directed from outer sphere towards inner sphere -- why is not that field zero?

  1. Inside it is zero, but outside it is present and that too only tangential?

  2. When we are talking about time varying fields, electric field is present inside a conductor only at inner surface or inside whole conductor? What will we answer when asked about the electric field inside a conductor in such case?

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  • $\begingroup$ Why did you said tangentially? Its perpendicular. $\endgroup$ – Anubhav Goel Apr 26 '16 at 10:08
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The $E$ inside a filled conductor is said to be zero only when at any point inside the closed surface the resultant of $E$ is $0$.

inside the inner conductor net electric field will always be zero because whole of the charge will reside only on its surface .(why)?

the reason is if there is any net $E$ at any point inside the inner conductor it will immediately pull the electrons in the opposite direction of $E$ due to charge on surface will increase which will decrease the $E$ which was present. the surface of conductor will absorb all the charge in such a way that net $E$ at any point inside inner conductor becomes zero.

1.Inside it is zero, but outside it is present and that too only tangential(i suspect it is tangential)?

remember the outer conductor has a hollow region and an another conductor inside it.if you consider a hypothetical gaussian surface enclosing the inner conductor only then there will be a net $E$ flux through that gaussian surface.this implies that resultant $E$ at points which lies on hollow region is not $0$.

Due to -ve charged inner conductor the +ve charge existing upon outer conductor will be attracted towards inner conductor .if -ve charge is more than +ve then the +ve charge on outer conductor will reside upon its inner surface and vice-verca.

2.Due to -ve charge on inner conductor there will be a net $E$ inside the outer conductor because of net charge inside outer conductor i.e $E$ inside the outer conductor is not $0$ in such case.

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Simplifying the questions into a single example, we can deal with a solid sphere. Isaac Newton's shell theorem serves our electrical domain nicely because electrical forces vary by the same inverse square range factor as the gravitational forces that acted upon Sir Isaac.

All of the electrical particles hosting the electrical charge upon the sphere form an outer shell that produces the same effective electrical field at the global center that would be present if all of the charged particles dwelt at the very center. If a test electron or proton were released near the sphere, one would repel away and the other would travel to the global center. Note that the imitating formations are mutually exclusive. Either case can be intuitively evaluated toward the same understanding.

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Consider a metal sphere of unit positive charge. Now , place a point charge at centre of sphere.

What do you observe?

You find that electric field inside sphere is not zero.

Why? Because , electric field due to charge on metal is cancelled and not by charge inside metal sphere.

Returning to your question

Similarly, Electric field due to positive charge on outer sphere is canceled in inter luminal space. But Field due to inner negative charge persists.

When we are talking about time varying fields, electric field is present inside a conductor only at inner surface or inside whole conductor?

It is present inside whole conductor, but more towards surface. Here E is directly proportional to R.

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