S₁ and S₂ are two hollow concentric spheres enclosing charges 2Q and 4Q respectively as shown in the figure.
(i) What is the ratio of electric flux through S₁ and S₂?
(ii) How will the electric flux through the sphere S₁ change, if a medium of dielectric constant 6 is introduced in the space inside S₁ in place of air?

Solution

(i) $Electric flux passing through first sphere, ϕ_{1} = \frac{2 Q}{ε_{0}} Electric flux passing through second sphere, ϕ_{2} = \frac{2 Q + 4 Q}{ε_{0}} = \frac{6 Q}{ε_{0}}$
$∴ ratio of flux through S_{1} and S_{2} is, \frac{ϕ_{1}}{ϕ_{2}} = \frac{2 Q}{ε_{0}} \times \frac{ε_{0}}{6 Q} = \frac{1}{3}$

(ii) If a medium of dielectric constant k is introduced then,
Using Gauss's theorem,

$ϕ_{1} = \oint \vec{E} \cdot \vec{ds} = \frac{2 Q}{ε_{0}}$
i.e, $ϕ'_{1} = \frac{1}{k} \oint \vec{E \cdot} \vec{ds}$

$= \frac{1}{k} \frac{2 Q}{ε_{0}} = \frac{1}{6} \frac{2 Q}{ε_{0}} = \frac{Q}{3 ε_{0}}$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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