An electrometer is charged to 3 kV. Then the electrometer is touched with a neutral metal ball, mounted on an isulating rod and then the metal ball is taken away and earthed The process is done for 10 times and finally the electrometer reads 1.5 kV. After this, at least how many times must the above process be repeated in order that the electrometer reads less than 1 kV?

Answer

`12`

Explanation

Initially `q_(1)=24(2/3muf)=16muC & q_(2)=16 muC`
Finally
`(V_(1)-24)xx1+(V_(1)-0)xx2+(V_(1)-24)xx2+(V_(1)-0)xx1=0`
`V_(1)(1+2+2+1)-24xx3=0 Rightarrow V_(1)=(24xx3)/6=12V`
`Q_(1)+Q_(2)=(12-24)xx1+(12-0)xx2=-12+24=12muC`
`Q_(3)+Q_(4)=(12-24)xx2+(12-0)xx1=-24+12=-12muC`
Initial net charge on plates left of S=0
Final net charge on plates left of `S=Q_(1)+Q_(2)=12 muC`
Charge flowing through `S=12 muC` towads left
Alternative `-2xx12xx1xx12=0=-12=12muC`