Suppose the spheres A and B have indentical sizes. A third sphere of the same size but uncharged is brought in contact with the first , then brought in contact with the second and finally removed from both. What is the new force of repulsion between A and B ?

Explanation

Now, the sphere C comes in contact with A, the charges will be divided equally on both spheres as they have same mass and size.

Now , charge on A is
` q_A = (q_A +q_C ) /( 2 ) , ( 6.5 xx 10 ^(-7) xx 0 )/(2)`
`= 3.25 xx 10 ^(-7) C `
Now , the charge on C will also be ` 3.25 xx 10^(-7) C`
` therefore " " q_C = 3.25 xx10 ^(-7) C`
Now, the sphere C comes in contact with B the charges are shared again
Now, charge on B is
` " " q_B = (q_B + q_C.)/(2) = (6.5 xx 10 ^(-7) + 3.25 xx 10 ^(-7))/(2)` < br> ` " " q_B = 4.875 xx 10 ^(-7) C `
Finally , the charge on C is
` " " q_C. = 4.875 xx 10 ^(-7)C `
Finally , the charge on A is
` " " q_A = 3.25 xx 10 ^(-7)C `
The charge on B is
` q_B = 4.875 xx 10 ^(-7)C `
From the Coulomb.s law, the force between two spheres,
` F = (1)/(4piin _0) . (q_A^(.).q_B^(.))/(r^(2))`
` (##ARH_CC_CHSE_ODI_PHY_XII_C01_E03_021_S02.png" width="80%">
` = (9xx 10 ^(9) xx 3.25 xx 10 ^(-7) xx 4.875 xx 10 ^(-7))/( (50 xx 10 ^(-2)) ^(2))`
` = (9xx3.25 xx 4.875 xx 10 ^(-5))/( 50 xx 50 xx 10 ^(_4))`
` rArr " " F= 5.7 xx 10 ^(-3) N`
This force will be repulsive in nature because both spheres have like charges.