A spherical ball with a charge of -6 µC is placed at the center of a hollow sphere. The hollow sphere has a charge of +12 µC. Illustrate the direction of electric field vectors inside and outside the hollow sphere.

Two charges, q₁ and q₂, are located at positions x = -0.2 m and x = +0.2 m, respectively. The charges have magnitudes of -8 μC and +2 μC, respectively. Determine the total electric flux through a cube of side 0.5 m centered at i) the origin ii) x = 0.3 m.

A point charge of -10 nC is located within a spherical metal shell that carries a total charge of 30 nC. What is the net charge on the i) internal (q_int) and ii) external (q_ext) surfaces of the shell?

A small ball with a net uniform positive charge of  50 nC and a radius of r = 0.2 cm is surrounded by a concentric thin spherical shell with a uniform negative charge of -50 nC and a radius of R = 1 cm. Find the net electric field (E) produced by the shell at the ball surface. 

A spherical asteroid produces a net electric flux of 5.26 × 10¹⁴ N•m²/C at its surface. Find the net charge (q_net) of the asteroid.

A student measures the strength of the electric field created by a small positively charged object at a distance of R = 0.2 m from it and comes up with a value of 2 × 10⁶ N/C. Find i) the electric flux (Φ_E) through a Gaussian sphere of radius R centered at the location of the object and ii) the charge (q) of the object.

Consider a scenario where four-point charges are positioned as illustrated in the figure. Sketch 2D cross-sectional views of closed surfaces intersecting these charges and yield an electric flux value of -3q/ε₀.