Two concentric shells have radii R and `2R` charges `q_A` and `q_B` and potentials `2V` and `(3/2)V` respectively. Now, shell B is earthed and let charges on them become `q_A'` and `q_B'`. Then,

Options

A. `q_A//q_B=1/2`
B. `q_A'//q_B'=1`
C. potential of AS after earhing becomes `(3/2)V`
D. potential difference between A and B after earting becomes `V//2`

Answer

A, D

Explanation

a. `V_A=2V=(kq_A)/R+(kq_B)/(2R)`
`V_B=3/2V=(kq_A)/(2R)+(kq_B)/(2R)`
solving these two equations we get
`q_A/q_B=1/2`
b.
`q_A^'/q_B^'=q_A/(-q_A)=-1`
c. & d. potential difference between A and B will remain unchanged as by earthing B, charge on will not changed.
`:. V_A^'-V_B^'=V_A-V_B`
`=2V-3/2V=V/2`
`:. V_A^'=V/2`
`as V_B^'=0`