Question

Same current $I$is flowing in three infinitely long wire 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)

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

Let the magnetic feild at a point for infinite wire be $B$.

Then, Here in this case contribution will come from wire along$x$ and $y$ axis only.

Which are perpendicular to each other.

So apply ampere circutal law and you can find direction and magnitude of $B$.

Let both are flowing along positive direction.

Then, magnetic field at $(-a)$ for $x$ would be

$\overrightarrow{B_x}=\frac{{\mu }_{0}I}{2\pi a}\hat{j}$

And for $y$ would be

$\overrightarrow{B_y}=\frac{{\mu }_{0}I}{2\pi a}-\hat{i}$

So the net magnetic field would be

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