Inductor

Inductor

A circuit element designed to provide self-inductance, typically in the form of a coil of wire.

Lenz’s law states that the induced emf always opposes the change in current.

What does Lenz’s law state for inductors?

The induced EMF acts in the opposite direction to resist the increase.

What happens when current is increasing in an inductor?

The induced EMF acts in the same direction as the current to oppose the decrease.

What happens when current is decreasing in an inductor?

If the current is constant, no EMF is induced.

What happens if the current is constant?

Traffic signals use inductors embedded in roads to detect vehicles by changes in inductance.

How do traffic signals use inductance?

Metal detectors use coils where induced emf changes due to nearby metal objects, allowing detection.

How do metal detectors use inductance?

Camera flashes use inductors and oscillators to generate high voltages that charge capacitors.

How do camera flashes use inductance?

L = ε/(d(I)/dt)

Mathematical Representation of Self-Inductance

Assume a current flowing through the inductor

What is the first step in solving self-inductance problems?

Determine the magnetic field produced by the current.

What is the second step in solving self-inductance problems?

Calculate the magnetic flux

What is the third step in solving self-inductance problems?

L = (N(Φ_m))/I

What is the fourth step in solving self-inductance problems?

B = (μ0)(N/l)(I)

Formula for magnetic field inside a long solenoid

Φ_m = BA = ((μ0)(N^2)A)/l

Formula for the magnetic flux through one turn of a solenoid

L = (μ0)(n^2)Al

Another form using turns per unit length n; Self-inductance can also be written as

Physical properties such as number of turns, geometry, and volume

What does solenoid inductance depend on?

B = ((μ0)NI)/(2πr)

Magnetic field inside a toroid

Because the magnetic field varies with radius

Why must flux be integrated in a toroid?

Φ_m = (((μ0)NhI)/(2π))ln(R2/R1)

Magnetic flux through a toroid

L = ((μ0)(N^2)h)/(2π))ln(R2/R1)

Self-inductance of a rectangular toroid?

Inductance represents how strongly a circuit resists changes in current.

What is the physical meaning of inductance?

current

Inductance in practical systems is determined entirely by geometry and material properties, not by _______.

i

(i)

R2

(ii)

R1

(iii)

r

(iv)

da

(v)

h

(vi)

dr

(vii)