A charged particle is suspended at the center of two thin concentric spherical charged shells, made of nonconducting material. Figure 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.
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What is the charge on the central particle?

Options

A. `0.2 muC`
B. `2 muC`
C. `1.77 muC`
D. `3.4 muC`

Answer

B

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.