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

Options

A. `-1`
B. `1`
C. `-(1)/(sqrt(2))`
D. `-2sqrt(2)`

Answer

D

Explanation

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`