- #1
Alex_Neof
- 41
- 2
Homework Statement
An infinitely long hollow cylinder of radius (a) carries a constant current (i). Use Biot - Savart's law and show that the magnetic field at the centre of the cylinder is zero.
Also show, using symmetry arguments and Ampere's law, the magnetic field is zero in any point inside the cylinder.
Homework Equations
Biot - Savart's law.
The Attempt at a Solution
[/B]
I know through symmetry and the right hand rule you get a magnetic field of zero at the centre, but how would one show this mathematically. I think evaluating a double integral would do this.
Firstly I evaluated an integral (with limits from 0 to pi) for the magnetic field at a perpendicular distance (a) from one straight infinitely long wire and obtained
B = (μ0)*(di) / 2*pi*a.
Where di is a fraction of the total current i for that one wire.
Now where I am finding difficulty is finding a way to evaluate the second integral for a circle for loads of wires which would produce an infinitely long hollow cylinder (cylindrical shell).
How would I produce the second integral ?
Thank you.
Update: second integral containing (μ0)*(di) / 2*pi*a. The limits would be from 0 to 2*pi