The total electric flux out of a closed surface surrounding a charge is given by Gauss's Law, which states that the electric flux through any closed surface is equal to the total charge enclosed divided by the permittivity of free space (ε0). The permittivity of free space is a constant value of approximately 8.85 × 10^-12 C^2/Nm^2.

The total electric flux (Φ_total) out of the closed surface (which in this case is the combination of the flat disk and the half-sphere) is given by:

Φ_total = Q / ε0

where Q is the charge enclosed.

Given that the charge Q is 7.8 μC = 7.8 × 10^-6 C, we can calculate the total electric flux:

Φ_total = (7.8 × 10^-6 C) / (8.85 × 10^-12 C^2/Nm^2) = 8.81 × 10^5 Nm^2/C

The problem states that the electric flux through the flat disk is 3.5 × 10^5 Nm^2/C. Therefore, the electric flux through the half-sphere (Φ_half-sphere) is the difference between the total flux and the flux through the disk:

Φ_half-sphere = Φ_total - Φ_disk
Φ_half-sphere = 8.81 × 10^5 Nm^2/C - 3.5 × 10^5 Nm^2/C = 5.31 × 10^5 Nm^2/C

So, the electric flux through the half-sphere is 5.31 × 10^5 Nm^2/C.

Question

The total electric flux out of a closed surface surrounding a charge is given by Gauss's Law, which states that the electric flux through any closed surface is equal to the total charge enclosed divided by the permittivity of free space (ε0). The permittivity of free space is a constant value of approximately 8.85 × 10^-12 C^2/Nm^2.

The total electric flux (Φ_total) out of the closed surface (which in this case is the combination of the flat disk and the half-sphere) is given by:

Φ_total = Q / ε0

where Q is the charge enclosed.

Given that the charge Q is 7.8 μC = 7.8 × 10^-6 C, we can calculate the total electric flux:

Φ_total = (7.8 × 10^-6 C) / (8.85 × 10^-12 C^2/Nm^2) = 8.81 × 10^5 Nm^2/C

The problem states that the electric flux through the flat disk is 3.5 × 10^5 Nm^2/C. Therefore, the electric flux through the half-sphere (Φ_half-sphere) is the difference between the total flux and the flux through the disk:

Φ_half-sphere = Φ_total - Φ_disk
Φ_half-sphere = 8.81 × 10^5 Nm^2/C - 3.5 × 10^5 Nm^2/C = 5.31 × 10^5 Nm^2/C

So, the electric flux through the half-sphere is 5.31 × 10^5 Nm^2/C.

Knowee AI · Accepted Answer

The total electric flux out of a closed surface surrounding a charge is given by Gauss's Law, which states that the electric flux through any closed surface is equal to the total charge enclosed divided by the permittivity of free space (ε0). The permittivity of free space is a constant value of approximately 8.85 × 10^-12 C^2/Nm^2.

The total electric flux (Φ_total) out of the closed surface (which in this case is the combination of the flat disk and the half-sphere) is given by:

Φ_total = Q / ε0

where Q is the charge enclosed.

Given that the charge Q is 7.8 μC = 7.8 × 10^-6 C, we can calculate the total electric flux:

Φ_total = (7.8 × 10^-6 C) / (8.85 × 10^-12 C^2/Nm^2) = 8.81 × 10^5 Nm^2/C

The problem states that the electric flux through the flat disk is 3.5 × 10^5 Nm^2/C. Therefore, the electric flux through the half-sphere (Φ_half-sphere) is the difference between the total flux and the flux through the disk:

Φ_half-sphere = Φ_total - Φ_disk
Φ_half-sphere = 8.81 × 10^5 Nm^2/C - 3.5 × 10^5 Nm^2/C = 5.31 × 10^5 Nm^2/C

So, the electric flux through the half-sphere is 5.31 × 10^5 Nm^2/C.

A particle with charge 7.8 μC is located inside a hemispherical bowl consisting of a half-sphere that shares its rim with a flat circular disks. If the electric flux through the flat disk is 3.5 × 105 Nm2/C3.5 × 105 Nm2/C , what is the flux through the half-sphere?

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