Physics Lesson 16.9.2 - Another Approach on Inductance

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Welcome to our Physics lesson on Another Approach on Inductance, this is the second lesson of our suite of physics lessons covering the topic of Inductance and Self-Induction, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Another Approach on Inductance

If a current I is flowing through the turns of a solenoid (called henceforth an "inductor"), it produces a magnetic flux Φm through the central region of the inductor. As a result, we obtain for the inductance of inductor in terms of magnetic flux:

L = N ∙ Φ_M/I

where N is the number of turns in the inductor. Indeed, since

L = μ₀ ∙ N² ∙ A/I

and

Φ_M = N ∙ B ∙ A

We obtain by combining the two above formulae (considering also the fact that the magnetic field of a solenoid is B = μ₀ ∙ N ∙ I/L)

L = N ∙ Φ_M/I
= N ∙ B ∙ A/I
= N ∙ μ₀ ∙ N ∙ I/L ∙ A/I
= μ₀ ∙ N² ∙ A/I

Therefore, the two formulae of inductance given above are equivalent.

Example 2

When a 10 cm long solenoid containing 200 turns and having the cross-sectional area of each turn equal to 4 cm₂ is connected to a 24 V power source. The resistance of the circuit is 48 Ω. What is the magnetic field the solenoid generates in such conditions?

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Clues:

l = 10 cm = 10^-1 m
N = 200 turns = 2 × 10² turns
A = 4 cm₂ = 4 × 10^-4 m²
ε = 24V
R = 48 Ω
(μ₀ = 4π × 10^-7 N/A²)
B = ?

Solution 2

First, we calculate the current flowing through the circuit through the Ohm's law. We have

I = ε/R
= 24 V/48 Ω
= 0.5 A

Now, let's calculate the inductance in the solenoid. We have

L = μ₀ ∙ N² ∙ A/I
= (4 ∙ 3.14 × 10^-7 N/A² ) ∙ (2 × 10² )² ∙ (4 × 10^-4 m² )/(10^-1 m)
= 2 × 10^-4 H

Now, let's use the other formula of inductance to find the magnetic field through the solenoid. Thus, giving that

L = N ∙ Φ_M/I = N ∙ B ∙ A/I

we obtain

B = I ∙ L/N ∙ A
= (0.5 A) ∙ (2 × 10^-4 H)/(2 × 10² ) ∙ (4 × 10^-4 m² )
= 1.25 × 10^-3 T
= 1.25 mT

You have reached the end of Physics lesson 16.9.2 Another Approach on Inductance. There are 3 lessons in this physics tutorial covering Inductance and Self-Induction, you can access all the lessons from this tutorial below.

More Inductance and Self-Induction Lessons and Learning Resources

Magnetism Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.9	Inductance and Self-Induction
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.9.1	The Meaning of Inductance
16.9.2	Another Approach on Inductance
16.9.3	Applications of Inductance in Technology

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