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Question

Two very thin metallic wires placed along X and Yaxes carry equal currents as shown in figure. AB and CD are lines at 45o with the axes. The magnetic fields will be zero on the line
166580_2156100a38984adc9e89e19edc6065bb.png
  1. CD
  2. segment OB only of line AB
  3. AB
  4. segment OC only of line CD

A
segment OB only of line AB
B
AB
C
segment OC only of line CD
D
CD
Solution
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All points on AB are equidistant from the two wires. So, magnetic fields are equal and opposite.
Thus, they cancel out.
All points on the wire CD are on either left side or right side of the wires AB and CD.
Hence, magnetic fields will not cancel.

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