Final answer:
The question requires the use of Gauss's Law to calculate the electric field inside a charged solid sphere with a spherical cavity at a certain distance from the center. By finding the charge enclosed by the Gaussian surface, accounting for both the point charge and the charge within the solid sphere, one can determine the electric field at the point of interest.
Step-by-step explanation:
The subject of the question is Physics, specifically the topic of electrostatics involving electric fields and charge distributions. Given a point charge of −3.0µC located at the center of a spherical cavity within a charged solid sphere with charge density ρ=7.35×10⁻⁴ C/m³, we are asked to calculate the electric field inside the solid at a distance of 9.5 cm from the center of the cavity. To calculate the electric field at this point, we can use Gauss's Law, where Π = Q/ε₀, and Q is the charge enclosed by the Gaussian surface.
First, we determine the total charge inside the Gaussian surface, including the charge from the solid sphere without the cavity. For the solid sphere part, the volume to consider is the volume of a sphere of radius 9.5 cm excluding the cavity of radius 6.5 cm. The total charge enclosed (Q) is the sum of the point charge and the charge due to the charge density within the solid sphere outside the cavity.
Calculation Steps:
- Calculate the volume of the solid sphere outside the cavity: V = (4/3)π((9.5 cm)³ - (6.5 cm)³).
- Calculate the charge in the solid sphere's volume: Q₁ = ρV.
- Add the point charge to the charge in the solid sphere: Q₀ = point charge + Q₁.
- Apply Gauss's Law to find the electric field: E(4πr²) = Q₀/ε₀, where E is the electric field, r is the distance from the center, and ε₀ is the permittivity of free space.
- Solve for the electric field: E = Q₀/(4πr²ε₀).
Finally, the electric field at 9.5 cm from the center is given by this equation. The direction of the electric field is radially outward from the center of the sphere because of the point charge's negative value.