In the shown figure a hemisphere is placed and two charges 3q and 9q are placed symmetrically about centre O. Net electric flux over curved surface is given as (N1 q/N2 ϵ 0), where N1 and N2 are lowest possible integers then value of N1+N2 is:

Question

In the shown figure a hemisphere is placed and two charges 3q and 9q are placed symmetrically about centre O. Net electric flux over curved surface is given as (N1 q/N2 ϵ 0), where N1 and N2 are lowest possible integers then value of N1+N2 is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-i8ajf5lyh8h1lole.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

According to Gauss's law of electrostatics, the net flux passing through the surface of hemisphere will be

ϕ = \frac{( 9 + 3 ) q}{ϵ _{0}}

Due to symmetry, the flux passing through the curved surface will be halfof the net flux. So,

ϕ = \frac{( 9 + 3 ) q}{2 ϵ _{0}} = \frac{6 q}{ϵ _{0}}

Q. In the shown figure a hemisphere is placed and two charges 3q and 9q are placed symmetrically about centre O. Net electric flux over curved surface is given as N2​ϵ0​N1​q​, where N1​ and N2​ are lowest possible integers then value of N1​+N2​ is :

According to Gauss's law of electrostatics, the net flux passing through the surface of hemisphere will be ϕ=ϵ0​(9+3)q​ Due to symmetry, the flux passing through the curved surface will be halfof the net flux. So, ϕ=2ϵ0​(9+3)q​=ϵ0​6q​

Q. In the shown figure a hemisphere is placed and two charges $3 q$ and $9 q$ are placed symmetrically about centre $O .$ Net electric flux over curved surface is given as $\frac{N _{1} q}{N _{2} ϵ _{0}},$ where $N_{1}$ and $N_{2}$ are lowest possible integers then value of $N_{1} + N_{2}$ is :

According to Gauss's law of electrostatics, the net flux passing through the surface of hemisphere will be
$ϕ = \frac{( 9 + 3 ) q}{ϵ _{0}}$
Due to symmetry, the flux passing through the curved surface will be halfof the net flux. So,
$ϕ = \frac{( 9 + 3 ) q}{2 ϵ _{0}} = \frac{6 q}{ϵ _{0}}$