Question

Same current $i$ is flowing in three infinitely long wires along positive x, y and z directions. The magnetic field at a point $(0,0,-a)$ would be

• A. $\frac{{\mu }_{0}i}{2\pi a}(\hat{j}-\hat{i})$
• B. $\frac{{\mu }_{0}i}{2\pi a}(\hat{i}+\hat{j})$
• C. $\frac{{\mu }_{0}i}{2\pi a}(\hat{i}-\hat{j})$
• D. $\frac{{\mu }_{0}i}{2\pi a}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

Answer: (A)

$\frac{{\mu }_{0}i}{2\pi a}(\hat{j}-\hat{i})$

Point $(0,0,-a)$ lies on x-axis, therefore magnetic field due to
current along z-axis is zero and due to rest two infinitely long wires is $\frac{{\mu }_0}{2\pi }\frac{1}{a}$.
Magnetic field due to current I in the x-direction is along y-direction.
Magnetic field due to current I in the ydirection is along -ve x-direction.
$\overrightarrow{B_{total}}=\frac{{\mu }_0}{2\pi }\frac{1}{a}(\hat{j}-\hat{i})$