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A thin spherical shell radius of r has a charge 2 uniformly distributed on it. At the centre of the shell, a negative point charge -q is placed. If the shell is cut into two identical hemi spheres, still equilibrium is maintained. Then find the relation between Q and q? |
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Answer» Solution :Here the outward electric PRESSURE at EVERY point on the shell due to its own charge is `P_1 = (sigma^2)/(2 in_0) ((Q)/(4pi r^2))^2 , P_1 = (Q^2)/(32 PI^2 in_0 r^4)` Due to -q, the electric field on the surface of the shell is `E = (1/(4 pi in_0) q/(r^2))`. This electric field pulls every point of the shell in inward direction. The inward pressure on the surface of the shell due to the negative charge is `P_2 = sigma E` `= ((Q)/(4 pi r^2)) (1/(4 pi in_0) q/(r^2)) = (QQ)/(16 pi^2 in_0 r^4)` For equilibrium of the hemispheircal shells `P_2 ge P_1` or `(Qq)/(16 pi in_0 r^4) ge (Q^2)/(32 pi^2 in_0 r^4) "" q ge (Q)/(2)`. |
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