Question

Four-point charges Q₁ = +17.7 μC, Q₂ = −8.85 μC, Q₃ = −17.7 μC and Q₄ = 35.4 μC are kept as shown in Figure 1 below.

Calculate electric flux emanating from the closed surface S.

Answer 1

According to the figure, only charges inside the boundary of S contribute to the flux. Charges outside the surface (Q₃ and Q₄) do not affect the total flux passing through it.

Given: Q₁ = +17.7 μC

Q₂ = −8.85 μC

Q₃ = −17.7 μC

Q₄ = 35.4 μC

Formula: `"Net Enclosed Charge" (Q_"enclosed") = Q_1 + Q_2`

= 17.7 + (−8.85)

= 17.7 − 8.85

= 8.85 μC

= 8.85 × 10⁻⁶ C

Gauss’s Law states that the total electric flux (Φ) through any closed surface is equal to the net charge enclosed within that surface `(Q_"enclosed")`divided by the permittivity of free space (ε₀):

`Φ_E = (Q_"enclosed")/ε_0`

= `(8.85 xx 10^-6 C)/(8.85 xx 10^-12 C^2//(N.m^2))`

= `8.85/8.85 xx 10^-6`

= 1 × 10⁻⁶ N . m²/C