Paragraph: The figure shows a circular loop of radius a with two...

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. Paragraph: The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2 ) all in the

Paragraph: The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2 ) all in the

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

Options

Acurrent in wire 1 and wire 2 is the direction PQ and RS, respectively and $h \approx a$
Bcurrent in wire 1 and wire 2 is the direction PQ and SR, respectively and $h \approx a$
Ccurrent in wire 1 and wire 2 is the direction PQ and SR, respectively and $h \approx 1.2a$
Dcurrent in wire 1 and wire 2 is the direction PQ and RS, respectively and $h \approx 1.2a$

Correct answer

C. current in wire 1 and wire 2 is the direction PQ and SR, respectively and $h \approx 1.2a$

Step-by-step solution

The net magnetic field at the given point will be zero if.

\left|{\overset{\to}{B}}_{wires}\right| = \left|{\overset{\to}{B}}_{loop}\right|

⇒ 2\dfrac{{\mu}_{0}I}{2\pi\sqrt{{a}^{2} + {h}^{2}}} \times \dfrac{a}{\sqrt{{a}^{2} + {h}^{2}}} = \dfrac{{\mu}_{0}I{a}^{2}}{2{\left({a}^{2} + {h}^{2}\right)}^{\dfrac{3}{2}}}

⇒ h \approx 1.2a

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