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Self Inductance

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Self Inductance

Coils of wire carrying current generate a magnetic field.

Strong field inside solenoid

If the current increases then the magnetic field increases.

Increased magnetic flux

The magnetic flux through all coils depends on the coil area and the number of turns.

NI,l

B

F

- The ratio of magnetic flux to current is the inductance.
- Inductance is measured in henrys.
- 1 H = 1 T m2 / A
- More common, 1 H = 1 V / A / s

- The inductance can be derived for an ideal solenoid.

An inductor is made by wrapping a single layer of wire around a 4.0-mm diameter cylinder. The wire is 0.30 mm in diameter.

What coil length is needed to have an inductance of 10 mH?

The formula is based on the radius and length of the coil.

Radius r = 2.0 x 10-3 m

Turns N = l / d

Substitute for N in the formula.

A changing current will create a changing flux.

Faraday’s law states that the changing flux will create an emf.

Direction from Lenz’s law

The emf acts to oppose the change in flux.

Inertial response

Increasing I, F

B

Decreasing I, F

B

Motors have internal coils.

The self-inductance will oppose a change in current by creating an emf.

This back-emf is responsible for excess power draw when a motor starts.

Faraday’s law gives the magnitude of the induced emf.

Depends on rate of change

The definition of inductance gives a relationship between voltage and current.

More useful in circuits

Inductive elements in a circuit act like batteries.

Stabilizes current

The definition of inductance applies to transformers.

Mutual inductance vs self-inductance

Mutual inductance applies to both windings.

- Electrical power is voltage times current.
- True for emf from inductance
- Average current is approximately one half maximum
- Use one half to get average power

- Magnetic energy is stored in a magnetic field.
- Energy is the power times the time

The energy density in a solenoid is based on its volume.

The energy density can be expressed in terms of the magnetic field.

The energy density in a capacitor is based on its volume.

The energy density can be expressed in terms of the electric field.

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