Part A:

The magnetic field within a solenoid is given by the formula

magnetic field = permeability of free space * (N/L) * I (*where N=number of turns, L=length, I=current)

permeability of free space = 4pi * 10^-7 T*m/A

I = 37 mA = 37*10^-3 A

N =425 turns

L = 11.5 cm = 11.5*10^-2 m

plugging into the formula for magnetic field we get

magnetic field = (4pi * 10^-7 T*m/A) * (425 / 11.5*10^-2 m) * (37*10^-3 A)

magnetic field = 1.72*10^-4 T = 172 µT

Part B:

Magnetic flux can be found by muliplying the magnetic field by the Area of the solenoid.

Area = pi*r^2

where r = (17/2) mm = (17/2)*10^-3 m

Area = pi*((17/2)*10^-3 m)^2

Magnetic flux = Magnetic field * Area

Magnetic flux = (1.72*10^-4 T )* pi*((17/2)*10^-3 m)^2

However since we are finding the magnetic flux through **each turn **we need to divide the answer by the total number of turns:

Magnetic flux through each turn= ((1.72*10^-4 T )* pi*((17/2)*10^-3 m)^2 ) / 425

Magnetic flux through each turn= 3.9*10^-8 T*m^2

Part C:

There are several ways to find the inductance.

The easiest way, since we already know the magnetic flux and the current, we can find inductance through the following formula:

Inductance = total magnetic flux / current

*we would need to multiply the magnetic flux through each turn by total number of turns to get back the total magnetic flux

Inductance = 425*(3.9*10^-8 T*m^2)* (37*10^-3 A)