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Question

$${q_1},{q_2},{q_3},\,{\text{and}}\,{q_4}$$ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss's law?
1016969_0b1630c35adf4fea80f1cd47e0e25149.png


A
5(E1+E2+E3).dA=q1+q2+q32ε0
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B
(E1+E2+E3).dA=(q1+q2+q3)ε0
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C
5(E1+E2+E3).dA=(q1+q2+q3+q4)ε0
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D
None of the above
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Solution

The correct option is B $$\oint_ {\left( {{{\overrightarrow E }_1} + {{\overrightarrow E }_2} + {{\overrightarrow E }_3}} \right).d\overrightarrow A = \dfrac{{\left( {{q_1} + {q_2} + {q_3}} \right)}}{{{\varepsilon _0}}}} $$
$$\oint { \overrightarrow { E } .\overrightarrow { ds }  } =\dfrac { { q }_{ enclosed } }{ { \varepsilon  }_{ 0 } } \\ \oint { \left( \overrightarrow { { E }_{ 1 } } +\overrightarrow { { E }_{ 2 } } +\overrightarrow { { E }_{ 3 } }  \right)  } .d\overrightarrow { A } =\dfrac { \left( { q }_{ 1 }+{ q }_{ 2 }+{ q }_{ 3 } \right)  }{ { \varepsilon  }_{ 0 } } $$

Physics

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