Consider a conducting spherical shell with
inner radius b = 0.862 m and outer radius c =
1.21 m. There is a net charge q2 = 3.82 ìC
on the shell. At its center, within the hollow
cavity, there is a point charge q1 = 2.89 ìC.
Determine the flux through the spherical
Gaussian surface S1, which has a radius of
a = 0.294 m.
Answer in units of Nm2/C
To determine the flux through the Gaussian surface S1, we can make use of Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the enclosed charge divided by the electric constant (ε₀).
The electric flux (Φ) can be calculated using the formula:
Φ = ∫ E · dA
where E is the electric field and dA is a differential area element. For a symmetric system like a conducting spherical shell, we can consider the electric field to be constant over the Gaussian surface. Therefore, the above equation simplifies to:
Φ = E * A
where E is the electric field magnitude and A is the area of the Gaussian surface.
In our case, the Gaussian surface S1 has a radius of a = 0.294 m.
To find the electric field at the surface of the Gaussian sphere, we consider two contributions: the electric field due to the charge q2 on the shell and the electric field due to the charge q1 at the center within the hollow cavity.
1. Electric field due to the charge q2 on the shell:
The electric field at any point outside a conducting spherical shell is zero. Therefore, there is no contribution to the electric field from the charge q2 on the shell. E₂ = 0.
2. Electric field due to the charge q1 at the center within the hollow cavity:
The electric field at any point inside a conducting hollow-cavity shell is zero. Therefore, there is no contribution to the electric field from the charge q1 at the center. E₁ = 0.
Since E₂ = 0 and E₁ = 0, the total electric field at the surface of the Gaussian sphere is also zero. Therefore, E = 0.
Now, the flux through the Gaussian surface S1 is given by:
Φ = E * A = 0 * A = 0 Nm²/C
Hence, the flux through the spherical Gaussian surface S1 is zero Nm²/C.