Five charges and are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss's law is given by . Which of the following statements is correct?

Question

Five charges $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$ are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss's law is given by $\oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$ . Which of the following statements is correct

Smart Achievers · Accepted Answer

(2)

According to Gauss's theorem in electrostatics, $\oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$ . Here, $E$ is due to all the charges $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$ . As $q$ is charge enclosed by the Gaussian surface, therefore, $q = q_{2} + q_{4}$

Solution

Q.
Five charges $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$ are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss's law is given by $\oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$ . Which of the following statements is correct

1 E on the LHS of the above equation will have a contribution from $q_{1}$ , $q_{5}$ and $q_{3}$ , while $q$ on the RHS will have a contribution from $q_{2}$ and $q_{4}$ only

2 E on the LHS of the above equation will have a contribution from all charges while $q$ on the RHS will have a contribution from $q_{2}$ and $q_{4}$ only

3 E on the LHS of the above equation will have a contribution from all charges while $q$ on the RHS will have a contribution from $q_{1}$ , $q_{3}$ and $q_{5}$ only

4 Both E on the LHS and $q$ on the RHS will have contributions from $q_{2}$ and $q_{4}$ only.

Ans.
(2)

According to Gauss's theorem in electrostatics, $\oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$ . Here, $E$ is due to all the charges $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$ . As $q$ is charge enclosed by the Gaussian surface, therefore, $q = q_{2} + q_{4}$

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Solution

Q. Five charges q1,q2,q3,q4 and q5 are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss's law is given by ∮E→·ds→=qε0. Which of the following statements is correct

1 E on the LHS of the above equation will have a contribution from q1, q5 and q3, while q on the RHS will have a contribution from q2 and q4 only

2 E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q2 and q4 only

3 E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q1, q3 and q5 only

4 Both E on the LHS and q on the RHS will have contributions from q2 and q4 only.

Ans. (2) According to Gauss's theorem in electrostatics, ∮E→·ds→=qε0. Here, E is due to all the charges q1,q2,q3,q4 and q5. As q is charge enclosed by the Gaussian surface, therefore, q=q2+q4