Question

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 ______.

1. `oint B.dl = +- 2μ_0I`
2. the value of `oint B.dl` is independent of sense of C.
3. there may be a point on C where B and dl are perpendicular.
4. B vanishes everywhere on C.

Options

• a and b

• a and c

• b and c

• c and d

Answer 1

b and c

Explanation:

Ampere’s law gives another method to calculate the magnetic field due to a given current distribution.

Line integral of the magnetic field `vecB` around any closed curve is equal to μ₀ times the net current i threading through the area enclosed by the curve, i.e.

`oint vecB * vec(dl) = mu_0 sumi = mu_0 (i_1 + i_3 - i_2)`

Total current crossing the above area is `(i_1 + i_3 - i_2)`. Any current outside the area is not included in net current. (Outward ⊙ → + ve, Inward ⊗ → – ve)

Applying the Ampere's circuital law, we have

`ointB* dl = i_0 (I - I) = 0` (because current is in opposite sense)

Also, there may be a point on C where B and dl are perpendicular and hence, `oint_c B*dl = 0`