The concept used here is Gauss’s law.
First use the gauss’s law to calculate the electric flux one face of the cube, then divide the flux through by 6 to get the flux through each of the six faces of the cube.
Finally, use the expression to calculate the flux through the cube when the length changes.
The Gauss’s law states that charge stored inside is equal to the flux times the permittivity of free space. It is expressed as follows:
Here, q is the charge, is the permittivity of free space, and is the flux through the surface.
(a)
Calculate the flux through one of the six faces of the cube.
The Gauss’s law states that charge stored inside is equal to the flux times the permittivity of free space. It is expressed as follows:
Here, q is the charge, is the permittivity of free space, and is the flux through the surface.
Rewrite the Gauss’s law for flux .
The expression to calculate the flux through the cube is,
Here, q is the charge, is the permittivity of free space, and is the flux through the surface.
The electric flux through one of the six faces of the cube is,
Substitute for , for in expression .
(b)
The electric flux through one of the six faces of the cube is,
Here, q is the charge, is the permittivity of free space, and is the flux through the surface.
From the expression, It is clear that the flux doesn’t depend on the side length.
Thus, the flux remains the same even the length of the cube sides changes.
Ans: Part aThe electric flux through one of the six faces of the cube is .
Part bThe electric flux through one of the six faces of the cube is .
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