What Is the Unit of Inductance (Henry) & How Does It Work?

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The unit of inductance, the henry (H), measures how quickly current establishes itself in an inductor when a voltage is applied. A higher inductance results in a slower rate of current change for a given voltage. The henry quantifies the relationship between the rate of current change and the voltage across the inductor, with one henry indicating a voltage of one volt causing a current change of one ampere per second. The discussion also touches on how inductance relates to magnetic flux and the effects of coil turns and core materials on current flow and back EMF. Overall, understanding inductance involves recognizing its impact on current behavior and magnetic field intensity in inductors.
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I read that the unit of inductance is the measure of the time it takes for a current to fully establish itself through the inductor.

When a battery is connected across a wire-coil inductor (or any kind of inductor), it
takes a while for the current flow to establish itself throughout the inductor. The current
changes at a rate that depends on the inductance: the greater the inductance, the
slower the rate of change of current for a given battery voltage.
The unit of inductance is an expression of the ratio between the rate of current
change and the voltage across an inductor. An inductance of one henry, abbreviated H,
represents a potential difference of one volt across an inductor within which the current
is increasing or decreasing at one ampere per second.

Is the reason it takes longer in some inductors for the current to establish itself because it creates a greater magnetic flux? Can the henry also tell you the intensity of the magnetic field produced in an inductor? Obviously a coil with 10 turns is going to have a greater magnetic flux than one with 5 turns. If I took the iron core out of the 10 turn coil would the current flow faster because there would be less back EMF? Is that the idea behind it? Wouldn't it be easier to measure an inductors inductance by measuring the magnetic flux created when current flows through it?

Have I got the right idea of the henry or am I mixing something up?
 
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You have the basic ideas correct. And the L value is generally easiest to measure by putting an AC voltage across the inductor, and measuring the resulting current. Measuring the flux directly is a more difficult physical problem.
 
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