Question

Two uniformly long charged wires with linear densities $\lambda $ and $3 \lambda $ are placed along $X$ and $Y$ axis respectively. Determined the slope of electric field at any point on the line $y=\sqrt{3} \, x$ .

• A. $3\sqrt{3}$
• B. $\frac{\sqrt{3}}{3 \sqrt{2}}$
• C. $\frac{1}{3 \sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

Answer: (C)

$E_{x}=\frac{3 \lambda }{2 \pi ϵ_{o} x}$
$E_{y}=\frac{\lambda }{2 \pi ϵ_{o} x \sqrt{3}}$
$\overset{ \rightarrow }{E}=\frac{3 \lambda }{2 \pi ε_{0} x}\hat{i}+\frac{\lambda }{2 \pi ε_{0} x \sqrt{3}}\hat{j}$
$Slope=\frac{E_{y}}{E_{x}}=\frac{\lambda /2 \pi \epsilon _{0} \sqrt{3} x}{3 \lambda /2 \pi \epsilon _{0} x}=\frac{1}{3 \sqrt{3}}$