Electric field inside conductor

Homework Statement

A spherical conducting shell of inner radius a and outer radius b contains a centrally-located point charge +Q. Is an electric field present at radii (i) less than a, (ii) between a and b, and (iii) greater than b?

The Attempt at a Solution

My textbook says the electric field inside a conductor (a<r<b here) is zero, but I can't understand why. In (i), the field is that due to the charge. In (iii), field lines emanate from the surface at right angles (because the induced charge is positive on the outer surface).

In (ii), it seems like the field should be non-zero because of the induced positive charge on the outer surface and the induced negative charge on the inner surface. Wouldn't this create an electric field directed radially inward from r=b to r=a? The textbook says it's zero.

cepheid
Staff Emeritus
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Homework Statement

A spherical conducting shell of inner radius a and outer radius b contains a centrally-located point charge +Q. Is an electric field present at radii (i) less than a, (ii) between a and b, and (iii) greater than b?

The Attempt at a Solution

My textbook says the electric field inside a conductor (a<r<b here) is zero, but I can't understand why. In (i), the field is that due to the charge. In (iii), field lines emanate from the surface at right angles (because the induced charge is positive on the outer surface).

In (ii), it seems like the field should be non-zero because of the induced positive charge on the outer surface and the induced negative charge on the inner surface. Wouldn't this create an electric field directed radially inward from r=b to r=a? The textbook says it's zero.