Magnetics 4 Question 11

12. When da 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 RS, respectively and ha (b) current in wire 1 and wire 2 is the direction PQ and SR, respectively and ha

(c) current in wire 1 and wire 2 is the direction PQ and SR, respectively and h1.2a

(d) current in wire 1 and wire 2 is the direction PQ and RS, respectively and h1.2a

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Answer:

Correct Answer: 12. (c)

Solution:

  1. BR=B due to ring

B1=B due to wire-1

B2=B due to wire-2

In magnitudes,

B1=B2=μ0I2πr

Resultant of B1 and B2

=2B1cosθ=2μ0I2πrhr=μ0Ihπr2

BR=μ0IR22(R2+x2)3/2=2μ0Iπa24πr3 As, R=a,x=h and a2+h2=r2

For zero magnetic field at P,μ0Ihπr2=2μ0Iπa24πr3

πa2=2rhh1.2a



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