1.

A charge Q is placed at each of the opposite corners of square. A chargeqis placed at each of the other two corners. If the net electrical force on Q is zero , then Q/q equals.

Answer»

`-1`
`1`
`-(1)/(sqrt(2))`
`-2sqrt(2)`

Solution :The charge ARRANGEMENT is shown in figure. Let side of square be `.l.then AC =lsqrt2`
As force `oversetto (F_(AC))` is repulsive HENCE for equilibrium `oversetto (F_(AB)) and oversetto (F_(AD))` must be attractive i.e.,q must be negative
As force`oversetto (F_(AC) ) ` is repulsive, hence for equilibrium `oversetto (F_(AB)) "and" oversetto (F_(AD)) ` must be attractive i.e.,q must be negative
` ""|oversetto ( F_(AC)) | = ( kQ^(2))/((lsqrt2)^(2)) =(kQ^(2))/( 2L^(2)) and |oversetto (F_(AB))| = | oversetto (F_(AD)) |=(kQ .q)/(l^(2))`
Then ` ""|oversetto(F_(AB)) +oversetto (F_(AD))| =sqrt(F_(AB) ^(2) +F_(AD)^(2) )= ( sqrt2kQq)/(l^(2)) `
` (##U_LIK_SP_PHY_XII_C01_E04_014_S01.png" width="80%">
SINCE ` ""oversetto (F_(AC) ) +oversetto (F_(AB)) +oversetto (F_(AD)) =0, "hence" |oversetto (F_(AC)) | =- |oversetto (F_(AB))+oversetto (F_(AD)) | `
` THEREFORE "" (kQ^(2))/( 2l^(2)) =-(sqrt2kQq)/(l^(2)) rArr (Q)/(q) =-2sqrt2`


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