Question

Three point charges, Q₁ = 30 nC, Q₂ = -150 nC, and Q₃ = 70 nC are enclosed by surface S. What net flux crosses S?

1. 150 nC
2. -150 nC
3. 50 nC
4. -50 nC

Answer 1

Correct Answer - Option 4 : -50 nC

Concept:

Gauss Law states that the net electric flux through a closed surface enclosing a volume equals the charge enclosed by it.

\(\mathop \oint \nolimits_s \overset{\rightharpoonup}{E}.\overset{\rightharpoonup}{{ds}} = \frac{Q}{{{\varepsilon _o}}}\)

Since D = ϵ0 E, we can write:

\(\mathop \oint \nolimits_s \overline D .\overset{\rightharpoonup}{{ds}} = Q\)

D̅ is the electric flux density.

Calculation:

Given: Q1 = 30 nC, Q2 = -150 nC, and Q3 = 70 nC, are enclosed by surface S.

Hence the net flux crosses surface S = total charge enclosed in the surface and the total charge enclosed is:

Q_enc = Net flux = Q₁ + Q₂ + Q₃

= 30nC + (-150nC) + 70nC

= - 50nC