Question

32.1 gauss law for magnetic fields
a hemispherical shell is placed in a uniform magnetic field of 0.050 t oriented so that the field is perpendicular to the base of the shell. which of the following statements is true?
the magnetic flux through the curved hemispherical surface is zero unless there is also an electric flux present.
the magnetic flux through the curved hemispherical surface is equal to that through the flat base.
the magnetic flux through the curved hemispherical surface is less than that through the flat base.
the magnetic flux through the curved hemispherical surface is greater than that through the flat base.

Explanation:

According to Gauss' Law for Magnetic Fields, $\Phi_B=\oint \vec{B}\cdot d\vec{A} = 0$ for a closed surface. Here, the hemispherical shell and its flat base together form a closed surface. The magnetic flux through the closed surface (hemispherical shell + flat base) is zero, i.e., $\Phi_{total}=\Phi_{curved}+\Phi_{flat}=0$. So, $\Phi_{curved}=-\Phi_{flat}$. The magnitude of the magnetic flux through the curved hemispherical surface is equal to that through the flat base.

Answer:

The magnetic flux through the curved hemispherical surface is equal to that through the flat base.