(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Field of long cylindrical shell conductor

1. The problem statement, all variables and given/known data

Shown above is the cross-section of a long cylindrical shell conductor of inner radius a=4.00 cm and outer radius b=7.00 cm which carries a current into the page.

The current density J (current/area) is uniform across the shell from r=a to r=b and has the magnitude J=3.6E3 A/m2 where r is the distance from the axis of the shell. (The magnitude of the total current carried by the conductor is thus given by I=J*π*(b2-a2)=37.3 A.)

(a) Find the magnitude of the magnetic field at r=2b=14 cm.

(b) Find the magnitude of the magnetic field at r=(a+b)/2=5.5 cm (halfway between the two shells).

(Hint: how much current is enclosed by the Amperian loop in each case?)

2. Relevant equations

B = (uIr)/(2pi*R^2) (inside conductor, r<R)

B = (uI)/2pi*r (outside conductor r>R)

where u = 4*pi*10^-7

3. The attempt at a solution

I already solved for part a, getting 5.33E-5 T using the second relevant equation.

But when I used the first relevant equation for part 1, I got 8.4 E-5 which I found out isn't correct. Here's how I did it:

(u*.055*37.3)/(2*pi*(.07^2)) = 8.4E-5 T.

What am I doing wrong?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Field of long cylindrical shell conductor

**Physics Forums | Science Articles, Homework Help, Discussion**