Electrostatics and Gauss's Law Concepts

What does Gauss's Law relate?

• Electric flux to enclosed charge

• Electric field to current

• Magnetic flux to resistance

• Voltage to capacitance

For a point charge 'q' enclosed by a spherical Gaussian surface, what is the charge enclosed (Q_in) used in Gauss's Law?

• 0

• q

• 2q

• 4πr²q

What is the electric field inside a metal conductor in electrostatic equilibrium?

• Directly proportional to the charge

• Inversely proportional to the charge

• Zero

• Dependent on the material's resistance

A point charge 'q' is placed inside a metal shell with a net charge 'Q'. If a Gaussian surface is drawn outside the metal shell, what is the total charge enclosed by this Gaussian surface?

• q

• Q

• q + Q

• 0

A metal shell with a net charge Q surrounds a point charge q at its center. What is the total charge enclosed by a Gaussian surface placed outside the metal shell?

• q

• Q

• q + Q

• q - Q

What is the electric field inside a solid metal shell that has a net charge Q, assuming no other charges are present inside the shell?

• Zero

• Proportional to Q

• Proportional to the distance from the center

• Dependent on the shell's thickness

An insulating sphere has a uniform charge density ρ. If a Gaussian surface is placed inside the sphere with a radius 'r' (where r < R, the sphere's radius), how is the charge enclosed related to the charge density?

• Q_enclosed = ρ * (4/3)πR³

• Q_enclosed = ρ * (4/3)πr³

• Q_enclosed = ρ * 4πr²

• Q_enclosed = ρ * 4πR²

An insulating charged shell has a total charge Q₀. The shell has an inner radius 'a' and an outer radius 'b'. What is the charge density (ρ) of the material in the shell?

• ρ = Q₀ / ((4/3)πb³)

• ρ = Q₀ / ((4/3)πa³)

• ρ = Q₀ / ((4/3)π(b³ - a³))

• ρ = Q₀ / (4π(b² - a²))