Electric lines of force about negative point charge are

Why do electric field lines not form closed loop ?

The electric field in a region is given $\vec E = a\hat i + b\hat j$ . Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to $y-z$ plane

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 charge $Q$ is fixed at a distance $d$ in front of an infinite metal plate. The lines of force are represented by

A charge $+q$ is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius $R_1$ and outer radius $R_2$. A charge $+Q$ is placed at a distance $r > R_2$ from the centre of the shell. Then the electric field in the hollow cavity