Question

Three infinitely long charged thin wires are placed along x, y, z axes. Their line charge densities are ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$ respectively. Then.

• A. $E_x$ at point $(a,a,0)$ is independent of ${\lambda }_2$
• B. $E_z$ at point $(a,a,0)$ is proportional to $\sqrt{{\lambda }_1^2+{\lambda }_2^2}$
• C. E at point $(a,a,0)$ is proportional to $\sqrt{{\lambda }_1^2+{\lambda }_2^2}$
• D. E in z direction at point $(a,a,0)$ is zero

Answer 1

The correct option is A $E_x$ at point $(a,a,0)$ is independent of ${\lambda }_2$

$E_y=\frac{2k{\lambda }_1}{a}+\frac{k{\lambda }_3}{a}$
$E_x=\frac{2k{\lambda }_2}{a}+\frac{k{\lambda }_3}{a}$
$\Rightarrow E=\sqrt{E_x^2+E_y^2}$
$E=\frac{k}{a}\sqrt{4{\lambda }_1^2+4{\lambda }_2^2+2{\lambda }_3^2+4{\lambda }_1{\lambda }_3+3{\lambda }_2{\lambda }_3}$