Question

A spherical surface completely surrounds a collection of charges. Find the electric flux (with its sign) through the surface if the collection consists of (a) a single +6.60 × 10-6 C charge, (b) a single -1.30 × 10-6 C charge, and (c) both of the charges in (a) and (b).

Answer 1

The electric flux through a spherical surface due to enclosed charges can be computed using Gauss's Law. The flux for a +6.60 x 10^-6 C charge is outward-directed, for a -1.30 x 10^-6 C charge it is inward-directed, and with both charges, the net flux is the sum of the individual fluxes.

Step-by-step explanation:

The student is asking about the concept of electric flux through a spherical surface that surrounds a collection of charges, which falls under the subject of Physics (specifically electromagnetism), and it is a high school- or introductory college-level question. According to Gauss's Law, the electric flux through a closed surface is directly proportional to the enclosed electric charge. This can be calculated using the formula Φ = q/ε0, where Φ is the electric flux, q is the electric charge, and ε0 is the permittivity of free space (approximately 8.85 x 10^-12 C2/N⋅m2).

For part (a), a spherical surface surrounding a single +6.60 × 10-6 C charge would result in an outward-directed electric flux Φ = +6.60 × 10^-6 C / 8.85 × 10^-12 C2/N⋅m2.

For part (b), a spherical surface surrounding a single -1.30 × 10-6 C charge would have an inward-directed electric flux Φ = -1.30 × 10^-6 C / 8.85 × 10^-12 C2/N⋅m2.

For part (c), when both charges are enclosed, their net flux through the surface is the sum of the individual fluxes. Therefore the net electric flux is Φ = (+6.60 × 10^-6 C - 1.30 × 10^-6 C) / 8.85 × 10^-12 C2/N⋅m2, which simplifies to the sum of the charges divided by the permittivity of free space.

Answer 2

(a) 6.8 x 10^5 Nm^2/C

(b) 1.47 x 10^5 Nm^2/C

(c) 5.3 x 10^5 Nm^2/C

Step-by-step explanation:

According to the Gauss's theorem

Electric flux = Charge enclosed / ∈0

(a) Charge enclosed = 6 x 10^-6 C

So, Electric flux = (6 x 10^-6) / (8.854 x 10^-12) = 6.8 x 10^5 Nm^2/C

(b) Charge enclosed = -1.3 x 10^-6 C

So, Electric flux = (1.3 x 10^-6) / (8.854 x 10^-12) = 1.47 x 10^5 Nm^2/C

(c) Charge enclosed = 6 x 10^-6 + (-1.3 x 10^-6) = 4.7 x 10^-6 C

So, Electric flux = (4.7 x 10^-6) / (8.854 x 10^-12) = 5.3 x 10^5 Nm^2/C