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Eight point charges (can be assumed as uniformly charged small
spheres and their centres at the corner of the cube) having value q
each are fixed at vertices of a cube. The electric flux through square
surface ABCD of the cube is
?
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Eight point charges (can be assumed as uniformly charged smallspheres ...
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Eight point charges (can be assumed as uniformly charged smallspheres ...


Calculation of Electric Flux through Square Surface ABCD of the Cube:

Electric flux through a surface is given by the formula:
Φ = ∫ E * dA

Where,
Φ = Electric flux
E = Electric field
dA = Area vector

Electric Field Due to Point Charges:
- The electric field due to a point charge q at a distance r is given by:
E = k * q / r^2
Where,
k = Coulomb's constant (k = 9 x 10^9 Nm^2/C^2)

Electric Field at the Center of the Cube:
- The electric field at the center of the cube is the vector sum of the electric fields due to all the point charges.
- Since the cube has symmetry, the electric field at the center of the cube will be along the diagonal of the cube.

Electric Flux through Square Surface ABCD:
- The electric flux through square surface ABCD of the cube can be calculated by considering the electric field at the center of the cube and the area vector of the square surface.
- Since the electric field is along the diagonal of the cube and the area vector is perpendicular to the square surface, the angle between the electric field and the area vector is 90 degrees.
- Therefore, the electric flux through square surface ABCD can be calculated as:
Φ = E * A * cos(90)
Φ = E * A

Conclusion:
- By calculating the electric field at the center of the cube due to the point charges and considering the area vector of square surface ABCD, the electric flux through the square surface can be determined.
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Eight point charges (can be assumed as uniformly charged smallspheres and their centres at the corner of the cube) having value qeach are fixed at vertices of a cube. The electric flux through squaresurface ABCD of the cube is?
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