Three large metal plates are arranged as shown. How much charge will flow through the key if it is closed ?
1 Answer
Let on the plate 1, given charge
The charges need to be redistributed as: Two surfaces facing each other must have equal and opposite charges. Now induction will take place due to the higher charge
Therefore,
This will lead to redistribution of charges on three electrically isolated plates before closing of the switch as shown in the figure below.
After closing of switch we see that plates 1 and 3 are at the same potential and plate 2 remains isolated. Let
Charge on isolated plate 2
#q_1+q_2=2Q# .......(1)
Potential between plates
#V_(21)=V_(23)#
#=>q_1/C_(1)=q_2/C_(2)# .....(2)
Now
#q_1=2q_2#
Inserting this in (1) and solving we get
#2q_2+q_2=2Q#
#q_2=(2Q)/3#
Also#q_1=(4Q)/3#
Charge moved through switch
#-Q/2-(-q_1)#
#=>-Q/2+(4Q)/3#
#=>(5Q)/6#