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Two insulated wires, carrying currents i1 and i2 wrapped over a conical frame form the coils 1 and 2. The distance of the apex from the plane of each ring is much much greater than the radius of the ring.  If they produce no net magnetic field at the apex P, the value of i1i2 is

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a

r2r1

b

r1r2

c

r1r22

d

r1r2

answer is B.

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Detailed Solution

B=μ0 4π   2Mx3  = μ0 4π  iπr2r/tan θ3 [Each ring behaves like a short magnetic dipole  .⇒  B ∝ ir,  ∴  B1 =B2 ⇒  i1r1  =i2r2  ⇒  i1i2  =r1r2
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Two insulated wires, carrying currents i1 and i2 wrapped over a conical frame form the coils 1 and 2. The distance of the apex from the plane of each ring is much much greater than the radius of the ring.  If they produce no net magnetic field at the apex P, the value of i1i2 is