Electric Fields and Charge Distribution

What is the primary difference in how charge is distributed in an insulating sphere compared to a conducting sphere?

• In a conducting sphere, charge is uniformly distributed throughout the volume; in an insulating sphere, it resides on the surface.

• In an insulating sphere, charge is uniformly distributed throughout the volume; in a conducting sphere, it resides on the surface.

• Charge is always uniformly distributed throughout the volume in both types of spheres.

• Charge always resides on the surface in both types of spheres.

Which equation correctly represents Gauss's Law for electric flux?

• E * A = Q_en / ε₀

• E / A = Q_en * ε₀

• E + A = Q_en - ε₀

• E - A = Q_en / ε₀

When calculating the charge enclosed (Q_en) by a Gaussian surface inside a uniformly charged insulating sphere, what ratio is used to determine the fraction of the total charge (Q) within the Gaussian surface?

• Ratio of surface areas (A_Gaussian / A_sphere)

• Ratio of radii (r_Gaussian / R_sphere)

• Ratio of volumes (V_Gaussian / V_sphere)

• Ratio of electric fields (E_Gaussian / E_sphere)

What is the formula for the electric field (E) inside a uniformly charged insulating sphere, where K is Coulomb's constant, Q is the total charge, r is the distance from the center, and R is the sphere's radius?

• E = K * Q / r²

• E = K * Q * r / R³

• E = K * Q * R / r³

• E = K * Q / R²

What are the standard SI units for volume charge density?

• Coulombs per square meter (C/m²)

• Coulombs per meter (C/m)

• Coulombs per cubic meter (C/m³)

• Newtons per Coulomb (N/C)

What is the volume charge density of an insulating sphere with a radius of 2m and a total electric charge of +50µC uniformly distributed throughout its volume?

• 1.49 x 10⁻⁵ C/m³

• 1.49 x 10⁻⁶ C/m³

• 1.49 x 10⁻⁷ C/m³

• 1.49 x 10⁻⁸ C/m³

What is the electric field 1.5m away from the center of an insulating sphere with a radius of 2m, given its volume charge density is 1.49 x 10⁻⁶ C/m³? (Use ε₀ = 8.85 x 10⁻¹² C²/(N·m²))

• 84,180 N/C

• 56,120 N/C

• 112,240 N/C

• 28,060 N/C

What is the electric field 3.0m away from the center of an insulating sphere with a radius of 2m and a total electric charge of +50µC? (Use k = 9 x 10⁹ N·m²/C²)

• 25,000 N/C

• 50,000 N/C

• 75,000 N/C

• 100,000 N/C