Magnetic field and current homework

[oddiseas]

Homework Statement

I have seen 4 different solutions to this question so I am starting to get confused.

A steady current I flows down a long cylindrical wire of radius R. Find the magnetic field, both inside and
outside the wire, if

(a) the current is uniformly distributed over an infinitely thin coaxial surface of radius R' < R within the wire.
(b) the current is distributed within the region r < R' such a way that j = a r3.
4

Homework Equations

The Attempt at a Solution

i have done part a0 but i am not sure about part b

Integrating i get I=2piar^5/5
Now other people have shown me 2pir^4/4,
but we are integrating an area da in cyllindrical coordinates so i am not sure what they are doing.

Then for the current enclosed in the cyllinder of radius R i get similarly. Then substituing the value for the constant a i get B=muIr^4/2piR^5 for r<R and B=muI/2piR for r>R

I am not sure if i have made any msiatkes

 

[diazona]

For the integral to find I, look at the units of the expression you got and of the expression other people have shown you. The two expressions have different units so they clearly can't both be right.

For the magnetic field, the split between the two expressions' domains shouldn't be at r=R. Also, in the last expression, you shouldn't have R in the denominator (but there should be something else in its place).