Find magnetic field of infinitely closely spaced loop

[cloudy14]

My lecturer ask us to think about this question.

Those loop are very closely spaced, with current I going in anticlockwise direction. The stack of loop have a total length of d. What is the magnetic field, B at the point X?

(I assume the X to be directly on top of the center of the loops.)

The attempt at a solution:

Help! I don't even know where to start. I tried to used the Ampere's Law
$$\oint{B \cdot dl}=\mu_0I_{enc}$$
But realized I ended up getting the results for a cylinder.

 

[NateD]

The solution:We can use Ampere's Law to calculate the magnetic field, B, at the point X. Since the current I is flowing in an anticlockwise direction, the integral will be taken clockwise around the loop. \oint{B \cdot dl} = \mu_0I_{enc}Where I_{enc} is the total current enclosed by the integral. In this case, the integral is taken around a single loop, and so I_{enc} = I. Thus:\oint{B \cdot dl} = \mu_0ISince we are looking for the magnetic field at the center of the loop, the distance dl is equal to the circumference of the loop, 2πr. Therefore,B = \frac{\mu_0I}{2\pi r}