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Gauss theorem: Gauss theorem is mainl...

Gauss theorem:
Gauss theorem is mainly used to find out the electric flux linked to a closed surface. It does not depend upon the shape or size of surface. According to this theorem, the electric flux linked to a closed surface is equal to `((1)/(epsilon_(0)))` times the charge enclosed by the surface.
Let we have a charge q, now if we want to find out the net flux linked to a closed surface around it them,
Electric flux `phi = oint_(s) vecE. vecds = (q)/(epsilon_(0))`
This theorem is applied over a....Surface:

A

Closed surface

B

Open surface

C

Both (a) and (b)

D

None of these

Text Solution

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The correct Answer is:
To solve the question regarding Gauss's theorem, we will follow these steps: ### Step 1: Understand Gauss's Theorem Gauss's theorem states that the electric flux (Φ) through a closed surface is proportional to the charge (q) enclosed within that surface. Mathematically, it is expressed as: \[ \Phi = \oint_{S} \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \] where: - \( \Phi \) is the electric flux, - \( \vec{E} \) is the electric field, - \( d\vec{s} \) is the differential area vector on the closed surface \( S \), - \( \epsilon_0 \) is the permittivity of free space. ### Step 2: Identify the Surface The question asks about the type of surface over which Gauss's theorem is applied. According to the theorem, it is applied over a closed surface. This means that the surface must completely enclose a volume. ### Step 3: Conclusion Based on the understanding of Gauss's theorem, we conclude that the theorem is applied over a closed surface. ### Final Answer Gauss's theorem is applied over a **closed surface**. ---
To solve the question regarding Gauss's theorem, we will follow these steps: ### Step 1: Understand Gauss's Theorem Gauss's theorem states that the electric flux (Φ) through a closed surface is proportional to the charge (q) enclosed within that surface. Mathematically, it is expressed as: \[ \Phi = \oint_{S} \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \] where: ...
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