Simple Solenoid Problem Solution Using Ampere's Law

[ABoul]

Homework Statement

the question can be found here: http://www.mailfreeonline.com/uploader/CED0D65C.jpg

Homework Equations

ampere's law

The Attempt at a Solution

a.
(is B the magnetic field?)
B = uI/L; u = 4pi x 10^-7, I = 1, L = 2pi x 0.1
so B = 2 x 10^-6

^ can anyone confirm this?

b. B = uNI/L (i'm guessing L is the radius this time). i don't know how to incorporate the length of the solenoid into this equation. i don't know the assumption either.

c. is this the same as part b but with numbers plugged in?

 

[Delphi51]

B = uNI/L (i'm guessing L is the radius this time)

An explanation of the letters should appear in your textbook where the formula is derived.
I looked in mine from the 1960's and it has B = uIn, where n is the number of turns per unit length. It looks like the value of B applies anywhere near the center of the coil.

My reading is that in (b) you have to derive the formula and in (c) use it to calculate the strength of the magnetic field. If your textbook doesn't have the derivation, you might look for a copy of my old Engineering Physics book - "Physics" by Halliday and Resnick. It is a big blue one. The derivation begins with Ampere's Law as a path integral.

 

[ABoul]

An explanation of the letters should appear in your textbook where the formula is derived.
I looked in mine from the 1960's and it has B = uIn, where n is the number of turns per unit length. It looks like the value of B applies anywhere near the center of the coil.

My reading is that in (b) you have to derive the formula and in (c) use it to calculate the strength of the magnetic field. If your textbook doesn't have the derivation, you might look for a copy of my old Engineering Physics book - "Physics" by Halliday and Resnick. It is a big blue one. The derivation begins with Ampere's Law as a path integral.

so B is constant anywhere inside the solenoid? that would make sense because the magnetic field is roughly a straight line when inside the solenoid as I've drawn it, but i still fail to see how the ratio of the length of the solenid and its diameter make a difference. also, is there a difference between "magnetic field" and "flux density"? i thought they were both given the symbol B.

 

[Gear300]

so B is constant anywhere inside the solenoid? that would make sense because the magnetic field is roughly a straight line when inside the solenoid as I've drawn it, but i still fail to see how the ratio of the length of the solenid and its diameter make a difference. also, is there a difference between "magnetic field" and "flux density"? i thought they were both given the symbol B.

The ratio between the diameter and length contribute to the idealization of the situation. If the diameter is comparable to the length, then the field lines in the solenoid are not "straight" enough for the equation to work.

Flux density sounds a bit funny. Its been a while since I've done this, so I may have simply forgotten what the term meant, but magnetic flux is the "bombardment" or flow of a magnetic field through an area. Flux density would depend on what density is being referred to (length, area, volume...); if its area, then it should technically simply be the magnetic field.