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If there existed only one type of charge q on the Earth, then what is the electric flux related to Earth?


1. Zero through any surface of Earth
2. Infinite flux on Earth
3. Zero if the charge is placed outside Earth and \(\frac{q}{\epsilon_0}\) if the charge is placed inside the Earth
4. Cannot be defined

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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:

  • 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.

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