Answer: (a) α =
(b) For r≤R: B(r) = μ_0.
For r≥R: B(r) = μ_0.
Explanation:
(a) The current I enclosed in a straight wire with current density not constant is calculated by:
where:
dA is the cross section.
In this case, a circular cross section of radius R, so it translates as:
For these circunstances, α =
(b) <u>Ampere's</u> <u>Law</u> to calculate magnetic field B is given by:
μ_0.
(i) First, first find for r ≤ R:
Calculating B(r), using Ampere's Law:
μ_0.
.μ_0
B(r) = .μ_0
B(r) = .μ_0
For r ≤ R, magnetic field is B(r) = .μ_0
(ii) For r ≥ R:
So, as calculated before:
I
Using Ampere:
B.2.π.r = μ_0.I
B(r) = .μ_0
For r ≥ R, magnetic field is; B(r) = .μ_0.