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Consider two hollow concentric spheres ,...

Consider two hollow concentric spheres , `S_(1)andS_(2)` enlosing charges 2Q and 4Q respectively as shown in the figure . (i) Find out the ratio of the electric flux through them (ii) How will the flux through the sphere `S_(1)` change if a medium of dielectric constant `epsilon_(r )` is introduced in the space inside `S_(1)` in place of air ? Deduce the necessary expression.

Text Solution

Verified by Experts

As per Guass . s theorem
Electric flux `=ointvecE,vecds=("Total charge enclosed")/(epsilon_(0))`
`therefore` For sphere `S_(1)` flux enclosed `=phi_(1)=(2Q)/(epsilon_(0))`
For spehre `S_(2)`, flux enclosed `=phi_(2)=(2Q+4Q)/(epsilon_(0))`
`=(6Q)/(epsilon_(0))`
`therefore(phi_(1))/(phi_(2))=(1)/(3)`
When a medium of dielectric consistant `epsilon_( r)` is introduced in the space inside sphere `S_(1)` the flux through `S_(1)` would be `phi_(1).=(2Q)/(epsilon_(r))`
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