To solve this problem, the concepts related to Magnetic Field and Inductance are necessary.
Our data are given by,
[tex]I = 40mA = 40*10^{-3}A[/tex]
[tex]N = 450turns[/tex]
[tex]d = 15mm = 15*10^{-3}m[/tex]
[tex]r = 7.5*10^{-3}m[/tex]
[tex]L = 12*10^{-12}m[/tex]
PART A) By definition we know that the magnetic field within a solenoid is defined as
[tex]B = \mu n I[/tex]
Where,
[tex]\mu =[/tex] Permeability constant
n = (N/L) Number of turns per meter
I = Current
Applying with our values we have that,
[tex]B = \mu_0 n I[/tex]
[tex]B = \mu_0 (\frac{N}{L})(I)[/tex]
[tex]B = (4\pi *10^{-7})(\frac{450}{12*10^{-2}})(40*10^{-3})[/tex]
[tex]B = 1.885*10^{-4} T[/tex]
PART B) The magnetic flux is defined by
[tex]\Phi = BA[/tex]
Where,
B = Magnetic Field
A = Area
[tex]\Phi = (1.885*10^{-4})(\pi(7.5*10^-3)^2)[/tex]
[tex]\Phi = 333.1*10^{-10} Tm^2[/tex]
PART C) For its part by definition the inductance in a solenoid is given by
[tex]L = \frac{N\Phi}{I}[/tex]
[tex]L = \frac{450(333.1*10^{-10})}{40*10^{-3}}[/tex]
[tex]L =0.3747*10^{-3}H[/tex]
[tex]L = 0.3747mH[/tex]
PART D) As can be seen in the three definitions and their respective formulas, both the inductance, the magnetic flux and the magnetic field would be affected and would also change
