Correct Answer - Option 3 : Zero if the charge is placed outside Earth and
\(\frac{q}{\epsilon_0}\) if the charge is placed inside the Earth
The correct answer is option 3) i.e. Zero if the charge is placed outside Earth and \(\frac{q}{\epsilon_0}\) if the charge is placed inside the Earth
CONCEPT:
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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.
CALCULATION:
- Earth can be considered as a closed surface.
According to Gauss's law, the total electric flux emerging out of a closed surface is \(ϕ = \frac{q}{ϵ_0}\).
- So if the charge q is placed inside Earth, the electric flux through Earth will be \( \frac{q}{ϵ_0}\)
- If the charge is placed outside the Earth, then the flux through Earth will be zero as q = 0.
Therefore, the correct answer is zero if the charge is placed outside Earth and \(\frac{q}{\epsilon_0}\) if the charge is placed inside the Earth.