Question

Find the total flux due to charge q associated with the given hemispherical surface

• A. $\left(a\right)\frac{q}{2{\epsilon }_0},\left(b\right)0,\left(c\right)\frac{q}{{\epsilon }_0},\left(d\right)0,\left(e\right)0$
• B. $\left(a\right)0,\left(b\right)\frac{q}{2{\epsilon }_0},\left(c\right)0,\left(d\right)\frac{q}{{\epsilon }_0},\left(e\right)0$
• C. $\left(a\right)\frac{q}{2{\epsilon }_0},\left(b\right)\frac{q}{{\epsilon }_0},\left(c\right)0,\left(d\right)\frac{q}{{\epsilon }_0},\left(e\right)0$
• D. $\left(a\right)0,\left(b\right)\frac{q}{2{\epsilon }_0},\left(c\right)0,\left(d\right)\frac{q}{{\epsilon }_0},\left(e\right)\frac{q}{{\epsilon }_0}$

Answer 1

Answer: (A)

$\left(a\right)\frac{q}{2{\epsilon }_0},\left(b\right)0,\left(c\right)\frac{q}{{\epsilon }_0},\left(d\right)0,\left(e\right)0$

In figure (b), (d), (e) , Total charge enclosed the surface is zero.

According to Gauss's Law

$\varphi =\int \overrightarrow{E}.\overrightarrow{d}l=\frac{q}{{\epsilon }_0}$

$\varphi =0$

${\varphi }_a=\frac{q}{2{\epsilon }_0}$

${\varphi }_c=\frac{q}{{\epsilon }_0}$

So, the correct option is A.