Question

Three semi-infinite wires, each carrying a current of $1 \, A$ are placed on each of the coordinate axes with their ends at the origin, as shown in the figure. The magnetic induction at point $P \, \left(- 2 \, m , 0 , 0\right)$ 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}}\left(\text { due to wire in } y-\text { axis) }=\frac{\mu_0 I}{4 \pi a} \hat{\mathrm{k}}\right. $
$ \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}})$