Ncert Exercises & Solutions

Two identical current-carrying coaxial loops carry current \(I\) in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as \(C,\)

(a)	\(\oint B\cdot dl= \mp 2\mu_0 I\)
(b)	the value of \(\oint B\cdot dl\) is independent of the sense of \(C\).
(c)	there may be a point on \(C\) where \(B\) and \(dl\) are perpendicular.
(d)	\(B\) vanishes everywhere on \(C\).

Which of the above statements is correct?

1.	(a) and (b)	2.	(a) and (c)
3.	(b) and (c)	4.	(c) and (d)

Hint: The magnetic field depends on the current.

Explanation: Consider a simple amperian loop passing once through both the identical current-carrying coaxial loops.
(i) According to Ampere circuital law, \(\oint_C \vec{B} \cdot d l=\mu_0(I-I)=0.\) Hence, option (a) is wrong.
(ii) As \(\oint_C \vec{B} \cdot d l=0,\) therefore \(\oint_C \vec{B} \cdot d l\) is independent of the sense of \(C.\) Thus option (b) is correct.
(iii) There will be a point on loop \(C,\) lying at the axis of two loops \(A\) and \(B,\) where \(\vec{B}\) and \(\vec{d}\) are perpendicular to each other. Thus option (c) is correct.
(iv) The value of \(\vec{B}\) does not vanish on various points of \(C.\)

Hence, option (3) is the correct answer.

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