Answer: [tex]\frac{16}{3}[/tex]π[tex]a^{3}[/tex] .
Given:
[tex]x^{2}+y^{2}+z^{2} \leq a^{2}, z \geq 0[/tex]
Using Gauss's Law = ∫∫s E ·dS
= ∫∫∫ div E dV,
⇒ Divergence (Gauss') Theorem
= ∫∫∫ (1+1+6) dV
= 8×(volume of the hemisphere, radius "a")
= 8× ([tex]\frac{1}{2}[/tex])(4/3)π[tex]a^{3}[/tex]
= [tex]\frac{16}{3}[/tex]π[tex]a^{3}[/tex] .
