Question

A point charge +q is at the origin. A spherical Gaussian surface centered at the origin encloses +q. So does a cubical surface centered at the origin and with edges parallel to the axes. Select "True" or "False" for each statement below.

1. Suppose (for this statement only), that q is moved from the origin but is still within both the surfaces. The flux through both surfaces is changed.

2.If the radius of the spherical Gaussian Surface is varied, the flux through it also varies.

3. The area vector and the E-Field vector point in the same direction for all points on the spherical surface.

4. The E-Field at all points on the spherical surface is equal due to spherical symmetry.

5. The Electric Flux through the spherical surface is less than that through the cubical surface.

I tried :( F , T, F, T, F) but it is wrong, and I don't know which one is wrong.

Answer 1

1.

Suppose (for this statement only), that q is moved from the origin but is still within both the surfaces. The flux through both surfaces remains unchanged.

True.
Again, the total electric flux through any closed Gaussian surface only depends on the net enclosed charge and the electric permittivity constant.

2. If the radius of the spherical Gaussian Surface is varied, the flux through it also varies.

False.
As per Gauss's law, the total electric flux through any closed Gaussian surface only depends on the net enclosed charge and the electric permittivity constant.

3.

The area vector and the E-Field vector point in the same direction for all points on the cubical surface.

False.
Area vectors point outward from the surface. The electric field vector points directly away from the enclosed positive charge. Only in the case of a Gaussian surface aligned with the "spread" of an electric field is this true.

4.

The E-Field at all points on the spherical surface is equal due to spherical symmetry.

True. I cannot comment any more than "spherical symmetry"

5.

The area vector and the E-Field vector point in the same direction for all points on the cubical surface.

False.
Area vectors point outward from the surface. The electric field vector points directly away from the enclosed positive charge. Only in the case of a Gaussian surface aligned with the "spread" of an electric field is this true.