Question

Three semi-infinite wires, each carrying a current of $1A$ are placed on each of the coordinate axes with their ends at the origin, as shown in the figure. The magnetic induction at point $P\left(-2m,0,0\right)$ is

• A. $\frac{{\mu }_0}{4\pi }(\hat{j}+\hat{k})$
• B. $\frac{{\mu }_0}{4\pi }(\hat{j}-\hat{k})$
• C. $\frac{{\mu }_0}{8\pi }(-\hat{j}+\hat{k})$
• D. $\frac{{\mu }_0}{8\pi }(\hat{j}+\hat{k})$

Answer 1

Answer: (C)

There is no magnetic field at $P$ due to wire in $x$ -axis ${\vec{B}}_{\mathrm{P}}(\text{ due to wire in }y-\text{ axis) }=\frac{{\mu }_{0}I}{4\pi a}\hat{\mathrm{k}}$
${\vec{B}}_{\mathrm{P}}\text{ (due to wire in }z-\text{ axis) }\frac{{\mu }_{0}I}{4\pi a}(-\hat{\mathrm{j}})$
$\therefore {\vec{B}}_{\mathrm{P}}=\frac{{\mu }_{0}I}{4\pi a}(-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
$=\frac{{\mu }_{0}I}{8\pi }(-\hat{\mathrm{j}}+\hat{\mathrm{k}})=\frac{{\mu }_0}{8\pi }(-\hat{\mathrm{j}}+\hat{\mathrm{k}})$