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A thin metallic spherical shell of radius R carries a charge Q on its surface . A point charge (Q)/(2) is placed at its centre C and an other charge +2 Q is placed outside the shell at a distance x from the centre as shown in the Fig . Find (i) the force on the charge at the centre of shell and at the point A , (ii) the electric flux through the shell . |
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Answer» Solution :(i) Force experienced by a CHARGE .q. when placed in an electric FIELD .E. is given by `F = q E`. As at centre C of the shell electric field is ZERO , hence force on the charge at the centre C is zero . At point A the electric field is due to charge `(Q)/(2)` and Q present on the SPHERICAL shell and has a value E = `(1)/(4 pi in_(0)) * (3Q)/(2x^(2))` `therefore` Force on the charge q = (2 Q)placed at A will be `F_(A) = qE = (2 Q) ((1)/(4pi in_(0)) (3Q)/(2x^(2))) = (1)/(4 pi in_(0)) (3Q^(2))/(x^(2))` (ii) The electric flux throughthe shell `phi_(E) = (1)/(in_(0))` (charge enclosed by the shell) `= (1)/(in_(0)) ((Q)/(2) + Q) = (3Q)/(2in_(0))` 
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