S1 and S2 are two hollow concentric spheres enclosing charges Q and 2Q respectively. (a) What is the ratio of electric flux through S1 and S2 (b) Instead of air if a medium of dielectric constant 5 is introduced inside S1, what will be the electric flux through it?

a) Flux through S1=Qε0; Flux through S2=Q+2Qε0=3Qε0Ratio of the flux is = 13b) Em=Eair/5New flux through S1=∮ E¯⋅ds¯=15∫E¯air⋅ds¯=15Qε0=Q5ε0

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S₁ and S₂ are two hollow concentric spheres enclosing charges Q and 2Q respectively.
(a) What is the ratio of electric flux through S₁ and S₂
(b) Instead of air if a medium of dielectric constant 5 is introduced inside S₁, what will be the electric flux through it?

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Detailed Solution

a) Flux through $S_{1} = \frac{Q}{ε_{0}}$ ; Flux through $S_{2} = \frac{Q + 2 Q}{ε_{0}} = \frac{3 Q}{ε_{0}}$
Ratio of the flux is = $\frac{1}{3}$
b) $E_{m} = E_{air} / 5$
New flux through $S_{1} = ∮ \bar{E} \cdot d \bar{s} = \frac{1}{5} \int {\bar{E}}_{air} \cdot d \bar{s} = \frac{1}{5} \frac{Q}{ε_{0}} = \frac{Q}{5 ε_{0}}$