What is the Magnetic Field Density at the Center of a Solenoid?

[abrowaqas]

Homework Statement

A solenoid has length L= 1.23m , and inner diameter d=3.55cm. it has five layers of windings of 850 turns each and carries a current i = 5.57 A. what B at its centre?

Homework Equations

B= Uo N I /L where Uo is permeability of free space.

The Attempt at a Solution

i first multiply 5 with 850 to get total number of turns

i-e N= 5*850

then i use the formula for solenoidal field
i-e
B= Uo NI/L

i am little confuse whether at centre it would be same and what about diameter given ?

kindly explain

 

[diazona]

Remember that the whole point of a solenoid (at least an ideal one) is that the magnetic field is the same at all points in its interior.

 

[abrowaqas]

diazona please explain your answer.
and kindly tell me that why the value of diameter is given in that problem. will it be used here or its just given to confuse?

 

[diazona]

diazona please explain your answer.

I don't see what there is to explain, beyond what I've already said. Can you elaborate on what you don't understand?

and kindly tell me that why the value of diameter is given in that problem. will it be used here or its just given to confuse?

That's for you to figure out. The diameter is available to you if you need it, but just because it's given doesn't mean you will need it.

 

[abrowaqas]

diazona as you said
Remember that the whole point of a solenoid (at least an ideal one) is that the magnetic field is the same at all points in its interior.

why it is same? that is what i am asking to explain.

thanks for the second part i got it..

 

[diazona]

You can use Ampere's law to prove that the magnetic field of an ideal infinite solenoid is the same at all points inside it, and zero everywhere outside. That's an exercise worth doing in itself, so you might want to try it.

 

[abrowaqas]

oh yes i got it.. even i have done it.. but didn;t remember.. thanks.. diazona..