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A solenoid 4.7 cm in diameter and 16.5 cm long has 102 turns and carries a current of 7.2 A. Find the magnetic flux through the circular cross-sectional area of the solenoid. Recall μ

0

=1.25664×10
−6
T⋅m/A. Answer in units of T

User DLobatog
by
8.2k points

1 Answer

6 votes

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.

User Sagar Jethi
by
7.9k points