In the diagram shown $P$ is a point negative charge. Its weight is balanced by the electric force due to the fixed very long wire. The equilibrium of the particle is,

A charge $q$ is placed at the centre of the cubical vessel (with one face open) as shown in the figure. The flux of the electric field through the surface of the vessel is,

A large sheet carries uniform surface charge density $\sigma$. A rod of length $2l$ has a linear charge density $\lambda$ on one half and $-\lambda$ on the second half. The rod is hinged at mid point $O$ and makes angle $\mathrm{\theta }$ with the normal to the sheet. The electric force experienced by the rod is,

The figure shows two large closely placed, parallel, non-conducting sheets with identical (positive) uniform surface charge densities, and a sphere with a uniform (positive) volume charge density. Four points marked as $1,2,3$ and $4$ are shown in the space in between. If $E_1,E_2,E_3$ and $E_4$ are magnitude of net electric fields at these points, respectively, then