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

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 ${\vec{E}}_P=\frac{2k\lambda }{a}(\hat{i}+\hat{j}+\hat{k})$