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A thin metallic spherical shell of radiu...

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 .

Text Solution

Verified by Experts

(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 through the shell `phi_(E) = (1)/(in_(0))` (charge enclosed by the shell)
`= (1)/(in_(0)) ((Q)/(2) + Q) = (3Q)/(2in_(0))`
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