A positive point charge \(q\) lies at the center of a spherical conducting shell carrying net charge \(\frac{3}{2} q .\) Sketch the field lines both inside and outside the shell, using eight field lines to represent a charge of magnitude \(q\).

Imagine a speck of dust carrying a tiny excess of positive charges—an example of what we call a positive point charge. In the realm of electrostatics, such a point charge generates an electric field that permeates the space around it outwardly. Why outwardly? Because the electric field represents the force that another positive charge would experience if placed within the influence of our point charge. Since like charges repel, the field arrows are drawn radiating away.

In visualizing this, we often use lines to depict the strength and direction of the electric field, called electric field lines. The convention is to have these lines originate from the positive charge, stretching outwards in a radial pattern. Each line corresponds to a certain amount of charge, and we proportionally represent more lines for a larger charge. For the scenario with charge 'q', eight lines suggest a moderate electric field strength, with each line symbolizing identical magnitudes.

• Electric field direction: Radiates outwards
• Line representation: More lines for larger positive charges
• Visualization principle: Field lines never cross

A spherical conducting shell, larger than our point charge, introduces a fascinating element into our electric playground. Conductors have free electrons that move easily throughout the material. Introduce an electric field, and these electrons organize themselves in response to eliminate the field within the conductor's body—this is a core principle of how conductors behave in an electric field.

When our conducting shell carries a net charge, it further complicates the situation. The shell's free electrons will redistribute until they reach a state where the electric field inside the shell is zero. But what does this look like? Well, all of the shell's excess charge, in this case, \(\frac{3}{2}q\), spreads uniformly on the outer surface. Why? Because like charges repel and seek the largest distance from each other, which is the outer surface in a shell. The inside surface has no excess charge. Thus, despite the internal point charge 'q', there are no field lines between them within the shell. This is due to electrostatic shielding, a remarkable behavior of conductors.

• Charge distribution: Uniform on the outer surface
• Electrostatic shielding: No electric field within the shell

Electrostatic equilibrium is a state where the sum of electric forces within a conductor is zero, leading to no net motion of charge. It can be a bit counterintuitive, but it's true—within a charged or uncharged conductor, electrons arrange themselvesto nullify electric fields in their sanctuary. This means, interestingly, that in our exercise with the spherical shell, there are no electric field lines within the metallic confines that stretch between the shell's inner surface and the central point charge.

But what about outside the shell? There, the story changes. The shell's external charge, \(\frac{3}{2}q\), happily contributes its electric field lines to the world beyond the shell—no different than if the shell were not there at all. So, for the external observer, it's just a larger charge sending out field lines in a radial fashion, indicating the forces a positive point charge would feel if placed in its vicinity.

• Zero net motion: Charge is at rest inside the conductor
• Internal electric field: Essentially non-existent
• External field lines: Indicative of combined charge 'q' and the shell's charge