Question

A sphere S1 of radius r
1
encloses a net charge Q. If there is another
concentric sphere S2 of radius r2
(r2
> r1
) enclosing charge 2Q, find the
ratio of the electric flux through S1 and S2
. How will the electric flux
through sphere S1
change if a medium of dielectric constant K is
introduced in the space inside S2
in place of air ?

Answer 1

A sphere of radius r₁ inclosed charge Q .
we know, according to Gauss theorem,
Electric flux is the ratio of net charge inclosed inside the Gaussian surface to permittivity of medium.
so, for sphere₁ , Electric Flux , Φ₁ = Q/ε₀ [ for vacuum medium ]

Similarly concenteric sphere of radius r₂ contains charge 2Q as shown in figure.
So, net charge inclosed inside the sphere₂ = Q + 2Q = 3Q
Hence, electric flux , Φ₂ = 3Q/ε₀ [ for vacuum medium ]

ratio of electric flux , Φ₁/Ф₂ = 1/3

Now, a medium of dielectric constant K is introduced in the space inside S₁ in place of air .
then, electric flux of S₁ = Q/2ε₀K , Means electric flux decreases K times in sphere₁

Answer 2

Answer:

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