Two similarly and equally charged idential metal spheres A and B repel each other with a force of ` 2 xx 10 ^(-5)) N. ` A third identical uncharged sphere C is touched with A and then , placed at the mid - point between A and B. Calculate the net electric force on C.

Explanation

Let charges on A and B be q each r be the distance between them. Then as shown in we have.
` F= ( 1)/(4 pi in _0) .(q^(2))/( r^(2)) =2 xx10 ^(-5) N. `
On touching C with A , charge on A as well as C will be `(q)/(2) `. Now
as shown in net force on C is
` " " F_C =|oversetto (F_(CA)) +oversetto (F_(CB))| =oversetto (F_(CB)) -oversetto (F_(CA)) =(1)/(4pi in _0) .(((q)/(2)) ((q)/(2)))/( ((r)/(2)) ) `
` =(1)/(4piin _0) [(2q^(2))/(r^(2)) -(q^(2))/(r^(2)) ]=(1)/(4 pi in _0) =2 xx 10 ^(-5) N ` along CA.
` (##U_LIK_SP_PHY_XII_C01_E09_003_S01.png" width="80%">