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.
The work done to "HOLD" a load of bricks at any height is zero.
Work is done only when force acts through a DISTANCE.
The work done to LIFT 30 kg of anything to 20m higher than
it already is, is
(force) · (vertical distance)
= (mass) · (gravity) · (vertical distance)
= (30 kg) · (9.8 m/s²) · (20 m)
= 5,880 joules
Explanation:
We have,
Spring constant of the spring, k = 165 N/m
Mass, m = 2 kg
It is required to find the period of the mass-spring system. For the spring mass system, the period is given by :

The frequency of vibration is reciprocal of its time period. So,

So, the period of the mass-spring system is 0.69 s and frequency is 1.44 Hz.