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A spherical conducting shell of inner ra...

A spherical conducting shell of inner radius `r_(1)` and outer radius `r_(2)` has a charge Q.
(a) A charge q is placed at the center of the shell. What is the surface charge density on the inner and outer surfaces of the shell ?
(b) Is the electric field intensity inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape ? Explain.

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### Step-by-Step Solution #### Part (a): Surface Charge Density on Inner and Outer Surfaces 1. **Understanding the Problem**: We have a spherical conducting shell with inner radius \( r_1 \) and outer radius \( r_2 \). A charge \( q \) is placed at the center of the shell, and the shell itself has a total charge \( Q \). 2. **Applying Gauss's Law**: According to Gauss's Law, the electric field \( E \) inside a conductor in electrostatic equilibrium is zero. Therefore, we can consider a Gaussian surface just inside the inner surface of the shell. ...
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