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Electric Charges and Fields — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields1 Mark
MCQ
For two statements are given-one labelled Assertion $(A)$ and the other labelled Reason $(R).$ Select the correct answer to these questions from the codes $(a), (b), (c)$ and $(d)$ as given below.
Assertion $(A):$ The electric flux emanating out and entering a closed surface are $8 \times 10^3$ and $2 \times 10^3\ Vm$ respectively. The charge enclosed by the surface is $0.053\ \mu\text{C}.$
Reason $(R):$ Gauss's theorem in electrostatics may be applied to verify.
  • ✓
    Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
  • B
    Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A.$
  • C
    $A$ is true but $R$ is false.
  • D
    $A$ is false and $R$ is also false.
✓

Answer

Correct option: A.
Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
According to Gauss's theorem in electrostatics, $\phi=\frac{\text{q}}{\epsilon_0}$
$\phi=\frac{\text{q}}{\epsilon_0}=8.85\times10^{-12}[8\times10^3-2\times10^3]$
$=53.10\times10^{-9}\text{C}$
$=0.053\ \mu\text{C}.$

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