A charge of magnitude Q is divided into two parts q and `(Q - q)` such that the two parts exert maximum force on each other. Calculate the ratio `Q//q`.

Options

A. `Q`
B. `(3Q)/(4)`
C. `(Q)/(2)`
D. `(Q)/(3)`

Answer

C

Explanation

By Coulomb's law,
When charge Q is dividied into two charges q and `Q-q`.
then
`F=(1)/(4pi epsilon_(0)).(q(Q-q))/(r^(2))`
`F_("max")=(1)/(4pi epsilon_(0)).((Q)/(2)(Q-(Q)/(2)))/(r^(2))`
(Putting `q=(Q)/(2),` for the maximum force)
`=(1)/(4pi epsilon_(0)).((Q)/(2)((Q)/(2)))/(r^(2))=(1)/(4pi epsilon_(0)).((Q^(2))/(4))/(r^(2))`
`=(1)/(4pi epsilon_(0)).(Q^(2))/(4r^(2))=(1)/(4pi epsilon_(0)).(Q^(2))/(4r^(2))=(1)/(4pi epsilon_(0)).(((Q)/(2))^(2))/(r^(2))`