Question

Two infinitely long charged wires with linear densities $\lambda $ and $3\lambda $ are placed along $x$ and y-axis respectively. Determine the slope of the 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)

$\overset{ \rightarrow }{E}=\frac{3 \lambda }{2 \pi \in _{0} x}\hat{i}+\frac{\lambda }{2 \pi \in _{0} x \sqrt{3}}\hat{j}$


$Slope= \, \frac{E_{y}}{E_{x}}=\frac{1}{\sqrt{3}}\div3=\frac{1}{3 \sqrt{3}}$