Question

A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is:

Answer 1

A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is μ₀ ( $\frac{N^2A}{l}$ ).

To find the answer, we need to know about the magnetic field due to a solenoid.

What is the magnetic field due to a solenoid?

• A solenoid is an insulated wire wound in the form of a helix.
• Its length is very large compared to its diameter.
• The magnetic field due to solenoid carrying current $I$ can be written as,

                             $B=$ μ₀n $I$

                               $n=\frac{N}{l}$

• We have an expression for magnetic flux as,

                            Φ $= BA$ Where, A is the area.

• Substituting above value of magnetic field in the expression of magnetic flux, we get,

                                       Ф $= \frac{NIA}{l}$ μ₀

• In terms of inductance, we can express the magnetic flux linked with the coil as,

                                        Ф $= LI$

• By equating above two equations of magnetic flux, we get the expression for inductance as,

                                        μ₀ ( $\frac{N^2A}{l}$ ) $I$  $=LI$

                                         $L=$ μ₀ ( $\frac{N^2A}{l}$ ).

Thus, we can conclude that the expression for inductance is  μ₀ ( $\frac{N^2A}{l}$ ).

Learn more about the solenoid here:

brainly.com/question/28058306

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