A metallic spherical shell has an inner radius \(R_1\) and an outer radius \(R_2.\) A point charge \(Q\) is placed at the center of the spherical cavity. What are the surface charge densities \(\sigma_{in}\) and \(\sigma_{out}\) on the inner and outer surfaces of the shell, respectively?
1. \(\sigma_{in} = -\dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=\dfrac{Q}{4\pi R_2^2}\)
2. \(\sigma_{in} = \dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=0\)
3. \(\sigma_{in} = 0,~ \sigma_{out}=\dfrac{Q}{4\pi R_2^2}\)
4. \(\sigma_{in} = \dfrac{Q}{4\pi R_1^2},~ \sigma_{out}=-\dfrac{Q}{4\pi R_2^2}\)
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