Discussion Forum



1)

The figure shows a circular loop of radius   $\alpha$  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 counter-clockwise direction if seen from above

2632021922_m10.JPG

 When d≈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


A) Current in wire 1 and wire 2 is the direction PQ and SR respectively and h=a

B) Current in wire 1 and wire 2 is the direction PQ and SR respectively and h=a

C) Current in wire 1 and wire 2 is the direction PQ and SR respectively and h=1.2 a

D) Current in wire 1 and wire 2 is the direction PQ and RS , respectively and h=1.2 a

Answer:

Option C

Explanation:

BR =B due to ring

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B1 = B due to wire-1

B2= B due to wire -2

 In magnitudes

     B1  =B2 =  $\frac{\mu_{0}l}{2\pi r}$

 Resultant of B1 and B2

$=2B_{1}\cos \theta =2\left(\frac{\mu_{0}l}{2\pi r}\right)\left(\frac{h}{r}\right)$

   = $\frac{\mu_{0}lh}{\pi r^{2}}$

   $B_{R}=\frac{\mu_{0}lR^{2}}{2(R^{2}+X^{2})^{3/2}}$

$=\frac{2\mu_{0}l\pi a^{2}}{4\pi r^{3}}$

   As , R=a ,x=h  and a2+h2=r2

 For zero magnetic field at P.

  $\frac{\mu_{0}lh}{\pi r^{2}}=\frac{2\mu_{0}l\pi a^{2}}{4\pi r^{3}}$

    $\Rightarrow$       $   \pi a^{2}=2rh\Rightarrow$ h≈1.2 a