Question

Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $xy-$plane as shown in figure.


These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $\text{P}$ will be:

• A. $\frac{+{\mu }_{0}I}{\pi d}\left(\hat{z}\right)$
• B. $-\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
• C. Zero
• D. $\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$

Answer 1

The correct option is C Zero

Let $B_1$ and $B_2$ are magnitudes of magnetic fields at point $\text{P}$ due to the conductors along $X$ and $Y$ axes, respectively.

$\Rightarrow \overrightarrow{B_1}=\frac{{\mu }_{0}I}{2\pi d}\left(\hat{k}\right)$

And, $\Rightarrow \overrightarrow{B_2}=\frac{{\mu }_{0}I}{2\pi d}(-\hat{k})$

The net magnetic field at $\text{P}$ is,

$\overrightarrow{B}=\overrightarrow{B_1}+\overrightarrow{B_2}$

$\overrightarrow{B}=\frac{{\mu }_{0}I}{2\pi d}(\hat{k}+(-\hat{k}\left)\right)=0$

Hence, $\left(A\right)$ is the correct answer.