91Ó°ÊÓ

a) The gaussian hemispherical surface of the radius,$\mathrm{R}=5.68 \mathrm{cm}$.

b) The magnitude of the electric field,$E=2.50N/C$.

Using the concept of the Gauss flux theorem, we can get the required value of the flux passing through the base area of the surface. Now, using the concept of the net charge to be zero for a Gaussian surface, we can get the electric flux through the curved surface.

Formula:

The electric flux passing through any surface, $\mathrm{ϕ}=\stackrel{→}{\mathrm{E}}.\stackrel{→}{\mathrm{A}}$ (i)

We choose a coordinate system whose origin is at the center of the flat base, such that the base is in the x-y plane and the rest of the hemisphere is in the$\mathrm{z}>0$ half-space.

Now, using the given data and area of the circular base,$\mathrm{A}={\mathrm{Ï€¸é}}^2$ in equation (i), we can get the electric flux through the base surface as given:

Hence, the value of the flux is $-0.0253 \mathrm{N}â‹\dots {\mathrm{m}}^2/\mathrm{C}$.

Since the flux through the entire hemisphere is zero, the flux through the curved surface is given as:

$$\begin{gathered} {\mathrm{Ï•}}_{\mathrm{C}}={\mathrm{Ï•}}_{\mathrm{base}} \\ =0.0253\mathrm{N}{\mathrm{m}}^2/\mathrm{C} \end{gathered}$$

Hence, the value of the flux is $0.0253\mathrm{N}{\mathrm{m}}^2/\mathrm{C}$.