Calculating the magnetic field of an infinite solenoid

[Adesh]

Homework Statement

Find the magnetic field at point P on the axis of a tightly wound solenoid (helical coil) consisting of n turns per unit length wrapped around a cylindrical tube of radius $a$ and carrying current $I$(Figure 25). Express your answer in terms of $\theta_1$ and $\theta_2$ (it's easiest that way). Consider the turns to be essentially circular, and use the result of example 6. What is the field on the axis of infinite solenoid (infinite in both directions) ?

Relevant Equations

$\tan \theta _1 = \frac{a}{z}$
$\tan \theta _2 = \frac{a}{l+z}$ where l is the length of the solenoid and z is the distance from the forward center to the point P.

Here is the image

$\tan \theta _1 = \frac{a}{z}$
$\tan \theta _2 = \frac{a}{l+z}$ where l is the length of the solenoid and z is the distance from the forward center to the point P.

My doubt is how $\theta_1$ going to become 0 and $\theta_2$ $\pi$ as the length of solenoid going to go to infinity. Please help me in seeing that.

 

[BvU]

My doubt is how $\theta_1$ going to become 0 and $\theta_2$ $\pi$ as the length of solenoid going to go to infinity. Please help me in seeing that.

In which expression would that be ?

 

[Adesh]

In which expression would that be ?

Homework statement states the question. Should I write it in the main body?

 

[BvU]

Find the magnetic field at point P on the axis of a tightly wound solenoid

So I expect you have an expression for the magnetic field at a point P in terms of $I, n, a, l$ and $z$, but expressed in $I, n, \theta_1$ and $\theta_2$. Post what you have worked out so far.

If the length of the coil is increased on both sides, $l$ and $z$ will go to infinity and P will be enveloped by the coil. What happens to $\theta_1$ and $\theta_2$ as 'defined' in the picture ?

 

[Adesh]

So I expect you have an expression for the magnetic field at a point P in terms of $I, n, a, l$ and $z$, but expressed in $I, n, \theta_1$ and $\theta_2$. Post what you have worked out so far.

If the length of the coil is increased on both sides, $l$ and $z$ will go to infinity and P will be enveloped by the coil. What happens to $\theta_1$ and $\theta_2$ as 'defined' in the picture ?

I have done it. My mistake was that I was considering that P will always be out of the solenoid at a distance of z but later I realized that P is fixed and as we increase the length of solenoid P will inside of it.