3. (a) A spherical conducting shell of radius R is grounded. A point charge -Qo is placed inside the shell on the z axis at z = do from the center. 1) Write down the Poisson's equation. [1] ii) Calculate the value ($Q_1$) and position ($d_1$) of the image charge, which will satisfy both the Poisson's equation and the boundary condition. [4] iii) Calculate the potential inside the shell in terms of R, $Q_0$ and $d_0$. [1] iv) Calculate the induced surface charge density on the conductor. [4]
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Poisson's Equation: The Poisson's equation relates the Laplacian of the electric potential (V) to the charge density (ρ) in a given region of space. In three-dimensional Cartesian coordinates, the Poisson's equation is given by: ∇²V = -ρ/ε₀ where ∇² is the Show more…
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