Final Answer:
The magnetic flux (
Φ
Φ) through the circular cross-sectional area of the solenoid can be calculated using the formula for the magnetic flux through a solenoid:
Φ
=
�
0
⋅
�
⋅
�
⋅
�
Φ=μ
0
⋅n⋅A⋅I
where:
�
0
μ
0
is the permeability of free space (
1.25664
×
1
0
−
6
�
⋅
�
/
�
1.25664×10
−6
T⋅m/A),
�
n is the number of turns per unit length (turns/m),
�
A is the cross-sectional area of the solenoid (m²),
�
I is the current flowing through the solenoid (A).
Calculation:
Find the number of turns per unit length (
�
n):
�
=
Total number of turns
Length of solenoid
n=
Length of solenoid
Total number of turns
Find the cross-sectional area (
�
A) of the solenoid:
�
=
�
(
Diameter
2
)
2
A=π(
2
Diameter
)
2
Substitute the values into the magnetic flux formula:
Φ
=
�
0
⋅
�
⋅
�
⋅
�
Φ=μ
0
⋅n⋅A⋅I
Result:
The magnetic flux through the circular cross-sectional area of the solenoid is approximately
6.47
×
1
0
−
3
T
⋅
m
2
6.47×10
−3
T⋅m
2
.
Step-by-step explanation:
The magnetic flux is a measure of the total magnetic field passing through a surface. In this case, the formula for the magnetic flux through a solenoid relates the permeability of free space, the number of turns per unit length, the cross-sectional area, and the current flowing through the solenoid. The calculation involves determining the values for
�
n and
�
A and then using them in the formula to find
Φ
Φ.