Physics - Electrostatics Question with Solution | TestHub

Each term is a two-dimensional line-charge field: $\frac{x\hat{i}+y\hat{j}}{x^2+y^2}$ belongs to a line along the z-axis, and its flux through a closed surface is $2\pi k$ times the length of that axis enclosed. Similarly for the other two terms along the x and y axes.

The ellipsoid $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ encloses axis segments $2a$, $2b$, $2c$.

$\Phi =2\pi k(2a+2b+2c)=4\pi k(a+b+c)$ ⇒ $n=4\pi \approx 12.566$.