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Question

Rank the magnitudes of B.dl for the closed paths a, b, c and d as shown in the figure. A long wire is located at the centre, perpendicular to the plane of the closed paths and carrying a current 1 A in outward direction.

A
c=a=d<b
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B
b<a=d=c
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C
a=d<c<b
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D
a=b=c=d
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Solution

The correct option is B b<a=d=c
According to Ampere circuital law,

B.dl=μ0ΣI

Where ΣI is net current passing through the loop.

Given, I=1 A is pointing outwards,

Considering the outward direction of current to be +ve, we traverse through all the loops in counter-clockwise sense.

For loop a, B.dl=μ0(1)=μ0 (ΣI=1 A)

For loop b, B.dl=μ0(0)=0 (ΣI=0)

For loop c,
B.dl=μ0(1)=μ0 (ΣI=1 A)

For loop d, B.dl=μ0(I)=μ0 (ΣI=1 A)

Hence,the correct order of B.dl for the four loops is,
a=d=c>b

Hence, option (b) is the correct answer.

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