What is the magnetic field of a solenoid and how does it change along the axis?

[Quantumcom]

Homework Statement

Consider a solenoid of length L and radius R, containing
N closely spaced turns and carrying a steady current
I. (a) In terms of these parameters, find the magnetic
field at a point along the axis as a function of distance
a from the end of the solenoid. (b) Show that as L
becomes very long, B approaches μoNI/2L at each end of
the solenoid.

Homework Equations

B=μoIR^2/2(x^2+R^2)^3/2

The Attempt at a Solution

let solenoid from y=0 to y=L and we can take solenoid as a formed of rings.
Consider a current loop of thickness dy, so current in that tiny ring= I(N/L)dy
But what is x? how to find it? I have no clue about it.If I have x then I can integrate 0 to L to find the total field..any idea?

 

[gneill]

Given your Relevant Equation and its use of x, isn't your solenoid's lengthwise axis lying along the x-axis? Thus x is the distance of any given "ring" to your point of interest along the x-axis where you want to know the field strength. It's up to you to place the solenoid and define the geometry so that x makes sense for what you're trying to solve. So, doesn't the solenoid extend from x=0 to x=L?

You might take a look here to see your Relevant Equation in a suitable context:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

In this case they show the current loop in the x-y plane, centered on the z-axis rather than the x-axis.

 

[WatermelonPig]

Draw a square Amperian loop which encloses a "side" of the solenoid.