Question

The electric field vector at point $P (a, a, a)$ due to three uniformly charged infinite wires $1, 2$ and $3$ kept the $x, y$ and $z$-axes, respectively as shown in shown in figure is (Charge unit length of each wire is $\lambda $ )

• A. $\frac{\lambda}{3 \pi \varepsilon_0 a}(\hat{i}+\hat{j}+\hat{k})$
• B. $\frac{2 k \lambda}{ a }(\hat{ i }+\hat{ j }+\hat{ k })$
• C. $\frac{\lambda}{2 \sqrt{2} \pi \varepsilon_{0} a}(\hat{i}+\hat{j}+\hat{k})$
• D. $\frac{\sqrt{2} \lambda}{\pi \varepsilon_0 a}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

Answer: (B)

The electric field vector at due to (2)
$\overrightarrow{\mathrm{E}}_2=\frac{\mathrm{k} \lambda}{\mathrm{a}}(\hat{\mathrm{i}}+\hat{\mathrm{k}})$ due to (3) $\vec{E}_3=\frac{k \lambda}{a}(\hat{i}+\hat{j})$
(1) $\vec{E}_1=\frac{k \lambda}{a}(\hat{j}+\hat{k})$
So $\vec{E}_P=\frac{2 k \lambda}{a}(\hat{i}+\hat{j}+\hat{k})$