Paragraph: The figure shows a circular loop of radius $a$ with two long parallel wires (numbered $1$ and $2$…

Paragraph: The figure shows a circular loop of radius $a$ with two long parallel wires (numbered $1$ and $2$ ) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is in the counterclockwise direction if seen from above.

Question: When $d \approx a$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case
  1. current in wire 1 and wire 2 is the direction PQ and RS, respectively and h≈a
  2. current in wire 1 and wire 2 is the direction PQ and SR, respectively and h≈a
  3. current in wire 1 and wire 2 is the direction PQ and SR, respectively and h≈1.2 a
  4. current in wire 1 and wire 2 is the direction PQ and RS, respectively and h≈1.2 a

Solution

The net magnetic field at the given point will be zero if.
B→wires=B→loop
⇒2μ0I2πa2+h2×aa2+h2=μ0Ia22a2+h232
⇒h≈1.2 a .

Asked in: JEE Advanced 2014 (Paper 2)

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