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Question

If the electric flux entering and leaving an enclosed surface respectively are Φ1 and Φ2, the electric charge inside the surface will be


A

(ϕ2ϕ1)εo

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B

(ϕ2+ϕ1)εo

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C

(ϕ1-ϕ2)εo

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D

εo(ϕ2ϕ1)

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Solution

The correct option is D

εo(ϕ2ϕ1)


Step1: Given data

Electric flux Φ1 (or electric field lines) entering a closed surface is negative, whereas electric flux Φ2 (or electric field lines) exiting a closed surface is positive.
As a result, net electric flux, Φ=(Φ2-Φ1)

Step2: Gauss's law

  1. The total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity, according to Gauss Law.
  2. The total flux associated with a closed surface equals 1εo times the charge encompassed by the closed surface, according to the Gauss law.

Step3: Applying gauss law

Φ=qinεoqin=εoΦqin=(Φ2-Φ1)εo

Hence, option D is the correct answer.


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