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.	$\oint B . dl = \mp 2 μ_{0} I$ .
b.	the value of $\oint B . dl$ 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 are correct?
1. a and b
2. a and c
3. b and c
4. c and d

(3) Hint: The magnetic field depends on the current.

Step 1: Applying the Ampere's circuital law, we have,

\oint_{c} B . d l = μ_{0} (I - I) = 0

(because the current is in the opposite sense.)

Step 2: Also, there may be a point on C where B and dl are perpendicular and hence;

\oint_{c} B . d l = 0

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