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Gauss's Law

q 1, q 2, q 3...

Question

$q_{1}, q_{2}, q_{3} a n d q_{4}$ are point charges located at points as shown in the figure and S is spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law.

A

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{2 ϵ_{0}}

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B

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}

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C

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3} + q_{4}}{ϵ_{0}}

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D

N o n e o f t h e a b o v e

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Solution

The correct option is B $\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}$
$\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}$
$q_{4}$ is outside the closed path.

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Similar questions

q_{1}, q_{2}, q_{3}

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 ?

Q. Assertion :Four point charges

q_{1}

q_{2}

q_{3}

q_{4}

are as shown in figure. The flux over the shown Gaussian surface depends only on charges

q_{1}

q_{2}

. Reason: Electric field at all points on Gaussian surface depends only charges

q_{1}

q_{2}

.

Q. Three point charges

- q_{1}

+ q_{2}

- q_{3}

are placed as shown in the figure. The x-component of force on

- q_{1}

is proportional to

(A)

: Four point charges

q_{1}, q_{2}, q_{3}

q_{4}

are as shown in figure. The flux over the shown gaussian surface depends only on charges

q_{1}

q_{2}

(R)

: Electric field at all points on gaussian surface is depends only on charges

q_{1}

q_{2}

Select the most appropriate answer from the options given below

\frac{1}{q_{1}} - \frac{x}{q_{1} q_{2}} + \frac{x^{2}}{q_{2} q_{3}} - \frac{x^{3}}{q_{3} q_{4}} + \dots

is equal to the continued fraction

\frac{1}{a_{1} +} \frac{x}{a_{2} +} \frac{x}{a_{3} +} \frac{x}{a_{4} +} \dots

q_{1}, q_{2}, q_{3}, \dots

are the denominators of the successive convergents.

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