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Question

Two wires having equal currents are placed perpendicular to each other as shown in the figure. Lines AB and 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 CD
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B
On AB
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C
On both OD and BO
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D
On both AB and CD
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Solution

The correct option is B On AB
Let us assume the
coordinate axis as shown in the figure.
For any point lying on CO,

B due to wire 1 and wire 2 points perpendicularly outwards ie (^k)

So, Bnet cannot be zero for any point lying on CO

For any point lying on OD,

B due to wire 1 and wire 2 points perpendicularly inwards. ie (^k)

So, Bnet cannot be zero for any point lying on OD

Now, For any point lying on OA,

B due to wire 1 points perpendicularly outards. ie (^k) and due to wire 2 points perpendicularly inwards.ie ^k

So, Bnet can be zero for any point lying on OA

Now, For any point lying on OB,

B due to wire 1 points perpendicularly inwards. ie (^k) and due to wire 2 points perpendicularly outwards.ie ^k

So, Bnet can be zero for any point lying on OB

Hence, option (b) is the correct answer.

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