Question

Three-Point charges enclosed by a surface 'S' are 10C, -5C, -5C. Find the total flux passing through 'S' 

1. \(\frac{20}{\epsilon _{0}}\)
2. \(\frac{10}{\epsilon _{0}}\)
3. \(\frac{5}{\epsilon _{0}}\)
4. 0

Answer 1

Correct Answer - Option 4 : 0

Concept:

Gauss's Law for electric field: 

It states that the total electric flux emerging out of a closed surface is directly proportional to the charge enclosed by this closed surface. It is expressed as:

\(ϕ = \frac{q}{ϵ_0}\)

Where ϕ is the electric flux, q is the charge enclosed in the closed surface and ϵ0 is the electric constant.

• The law implies that the total electric flux through a closed surface is zero, if no charge is enclosed by the surface,
• Gauss law is true for any closed surface, no matter what its shape or size
• The charge 'q' includes the sum of all charges enclosed by the surface

 

Calculation:

Given:

q₁ = 10C, q2 = -5C, and q3 = -5C

Total charge inside the surface

⇒ S = 10+ (-5) + -(5) = 0 C

Therefore, from Gauss law 

\(\Rightarrow Total \, \, flux (\phi)=\frac{q_{net}}{\epsilon _{0}}=0\)

Hence the correct option is 4