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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))`
Gauss theorem is used to find out:

A

Electric force

B

Electric flux

C

Electric potential

D

None of these.

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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 total electric flux (Φ) through a closed surface is proportional to the charge (q) enclosed within that surface. Mathematically, it can be expressed as: \[ \Phi = \oint_{S} \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \] Where: - \(\Phi\) is the electric flux through the closed surface. - \(\vec{E}\) is the electric field vector. - \(d\vec{s}\) is the differential area vector on the closed surface. - \(q\) is the total charge enclosed within the surface. - \(\epsilon_0\) is the permittivity of free space. ### Step 2: Identify the Purpose of Gauss's Theorem From the passage, we can see that the main purpose of Gauss's theorem is to find the electric flux linked to a closed surface. This is independent of the shape or size of the surface. ### Step 3: Apply the Theorem to a Charge If we have a charge \(q\) placed inside a Gaussian surface, we can use Gauss's theorem to calculate the electric flux linked to that surface. The equation simplifies to: \[ \Phi = \frac{q}{\epsilon_0} \] ### Step 4: Conclusion Thus, Gauss's theorem is primarily used to find out the electric flux linked to a closed surface surrounding a charge. ### Final Answer Gauss's theorem is used to find out the electric flux linked to 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 total electric flux (Φ) through a closed surface is proportional to the charge (q) enclosed within that surface. Mathematically, it can be expressed as: \[ \Phi = \oint_{S} \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \] ...
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