Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0 \times 10^{3} \;Nm ^{2} / C .$

$(a)$ What is the net charge inside the box?

$(b)$ If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

Using thomson's model of the atom, consider an atom consisting of two electrons, each of charge $-e$, embeded in a sphere of charge $+2e$ and radius $R$. In equilibrium each electron is at a distance $d$ from the centre of the atom. What is the equilibrium separation between electrons

Obtain Gauss’s law from the flux associated with a sphere of radius $\mathrm{'r'}$ and charge $\mathrm{'q'}$ at centre.

In figure a point charge $+Q_1$ is at the centre of an imaginary spherical surface and another point charge $+Q_2$ is outside it. Point $P$ is on the surface of the sphere. Let ${\Phi _s}$be the net electric flux through the sphere and ${\vec E_p}$ be the electric field at point $P$ on the sphere. Which of the following statements is $TRUE$ ?