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?

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

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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