A charge of -9C is placed at the center of a concentric spherical shell made of a linear dielectric material (relative permittivity 9) and having inner and outer radii of 0.1m and 0.2m, respectively. The total charge induced on its inner surface is how many C (Rounded off to two decimal places).?

Question

Answer

Understanding the Problem
A charge of -9C is placed at the center of a concentric spherical shell made of a linear dielectric material with a relative permittivity of 9. The inner radius of the shell is 0.1m, and the outer radius is 0.2m. We need to determine the total charge induced on the inner surface of the shell.
Key Principles
- Gauss's Law: This law states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.
- Induced Charge: When a charge is placed inside a dielectric, it induces a charge on the inner surface of the dielectric.
Calculating the Induced Charge
- Enclosed Charge: The charge at the center is -9C.
- Dielectric Effects: The dielectric does not change the total induced charge but affects the electric field inside the dielectric.
- Induced Charge Calculation: Since the inner surface of the shell must neutralize the electric field from the -9C charge, it will acquire a charge equal in magnitude but opposite in sign.
Result
- Therefore, the total charge induced on the inner surface of the spherical shell is:
- Total induced charge = +9C
Thus, the total charge induced on the inner surface of the shell is 9.00 C (rounded off to two decimal places).
This ensures that the electric field inside the conductor remains zero, adhering to electrostatic equilibrium principles.

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