A charged particle is suspended at the centre of two thin concentric spherical charged shells, made of non conducting material. Figure A shows cross section of the arrangement. Figure B gives the net flux `phi` through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere.

What is the charge on shell A ?

Options

A. `5.31muC`
B. `-5.31muC`
C. `-3.54muC`
D. `-1.77muC`

Answer

C

Explanation

We see that `phi` remains constant up to `r_(1)`. So `r_(1)ltr_(A)`. Let q be the charge at centre than
`phi=(q_("in"))/(epsilon_(0))` or `2xx10^(5)=(q)/(8.85xx10^(-12))` or `q=1.77muC` ltBrgt Similarly `phi=-4xx10^(5)=(q+q_(A))/(epsilon_(0))" " q_(A)=-5.31muC`
Where `q_(A)` is the charge on A. electric field is zero nowhere as `phi` is not zero anywhere.