A point charge of 17.7micro coulomb is located at the centre of a cube of side 0.03metre.Find the electric flux through each surface of the cube.?

Question

Answer

Given

Charge, q = 17.7 micro coulomb

Side of cube, a = 0.03 metre

Concepts Used

Electric Flux

Gauss's Law

Explanation

The electric flux through each surface of the cube can be found using Gauss's law. According to Gauss's law, the electric flux through a closed surface is proportional to the charge enclosed within the surface.

We can choose a cube of any size that encloses the point charge. In this case, we are given a cube with side a = 0.03 metre. We can imagine a Gaussian surface in the form of a cube with side a and passing through the centre of the given cube. The charge enclosed within this Gaussian surface is q = 17.7 micro coulomb.

The electric flux through each surface of the cube is given by:

ϕ = E x A

where E is the electric field and A is the area of the surface.

Since the electric field is constant and perpendicular to the surfaces of the cube, the electric flux through each surface is the same.

Using Gauss's law, we can find the electric field at any point outside the point charge. The electric field at a distance r from the point charge is given by:

E = q / (4πε₀r²)

where ε₀ is the permittivity of free space.

Substituting the given values, we get:

E = (17.7 x 10^-6) / (4π x 8.85 x 10^-12 x (0.03/2)²) = 1.72 x 10⁷ N/C

The area of each surface of the cube is a². Therefore, the electric flux through each surface is:

ϕ = E x A = (1.72 x 10⁷) x (0.03)² = 4.14 x 10³ Nm²/C

Answer

The electric flux through each surface of the cube is 4.14 x 10³ Nm²/C.

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