- Home
- Standard 12
- Physics
A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a / 4,0),+$ $3 q$ at $(0,0,0)$ and $-q$ at $(0,+a / 4,0)$. Choose the correct option$(s)$.
$(A)$ The net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-a / 2$.
$(B)$ The net electric flux crossing the plane $y=+a / 2$ is more than the net electric flux crossing the plane $y=-a / 2$
$(C)$ The net electric flux crossing the entire region is $\frac{q}{\varepsilon_0}$.
$(D)$ The net electric flux crossing the plane $z=+a / 2$ is equal to the net electric flux crossing the plane $x=+a / 2$.
$(A,B,C)$
$(A,B,D)$
$(A,C,D)$
$(B,C,D)$
Solution
Position of all the charges are symmetric about the planes $x=\frac{+a}{2}$ and $x=\frac{- a }{2}$. So net electric flux through them will be same.
Similarly flux through $y =\frac{+ a }{2}$ is equal to flux through $y =\frac{- a }{2}$.
$\phi=\frac{q_{\text {in }}}{\varepsilon_0}=\frac{3 q-q-q}{\varepsilon_0}=\frac{q}{\varepsilon_0}$
By symmetry flux through $z=\frac{+a}{2}$ is equal to flux through $x=\frac{+a}{2}$
