Question

Two wires having equal currents are placed perpendicular to each other as shown in the figure. Lines $\text{AB}$ and $\text{CD}$ are perpendicular to each other and symmetrically placed with respect to the current carrying wires. Where can we expect the resultant magnetic field to be zero?

• A. On $\text{CD}$
• B. On $\text{AB}$
• C. On both $\text{OD}$ and $\text{BO}$
• D. On both $\text{AB}$ and $\text{CD}$

Answer 1

The correct option is B On $\text{AB}$

Let us assume the
coordinate axis as shown in the figure.
For any point lying on $\text{CO}$,

$\overrightarrow{B}$ due to wire $1$ and wire $2$ points perpendicularly outwards ie ($\hat{k}$)

So, ${\overrightarrow{B}}_{net}$ cannot be zero for any point lying on $\text{CO}$

For any point lying on $\text{OD}$,

$\overrightarrow{B}$ due to wire $1$ and wire $2$ points perpendicularly inwards. ie ($-\hat{k}$)

So, ${\overrightarrow{B}}_{net}$ cannot be zero for any point lying on $\text{OD}$

Now, For any point lying on $\text{OA}$,

$\overrightarrow{B}$ due to wire $1$ points perpendicularly outards. ie ($\hat{k}$) and due to wire $2$ points perpendicularly inwards.ie $-\hat{k}$

So, ${\overrightarrow{B}}_{net}$ can be zero for any point lying on $\text{OA}$

Now, For any point lying on $\text{OB}$,

$\overrightarrow{B}$ due to wire $1$ points perpendicularly inwards. ie ($-\hat{k}$) and due to wire $2$ points perpendicularly outwards.ie $\hat{k}$

So, ${\overrightarrow{B}}_{net}$ can be zero for any point lying on $\text{OB}$

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