Inductance

Made by Mackenzie Rideout

Short Description of Topic

The Main Idea

Inductance is when a current from one coil causes current in a second, coil that is not connected to the original current or coil. A similar affect also happens within singular coils. A coil with current running through it will cause a current in the opposing direction to form. This opposing current actually works to slow down the original current. Because of these opposing currents the original current becomes almost sluggish. This quality is what makes it difficult to increase or decrease any current. Inductance is commonly found in circuits that contain a solenoid.

A Mathematical Model

To be able to successfully compute the inductance of a coil you will have to analyze the magnetic field that surrounds it. In the case of a solenoid, the magnetic field is B=μ0NI/d. For a solenoid this can give you information about the current running through one loop on the solenoid which you can then use to find the current that is running through the entire solenoid from beginning to end. You do this by taking the derivative of the magnetic field with respect to time and then multiplying this result by the number of loops in the solenoid.

A Computational Model

Here is a visual display of inductance in a solenoid

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Emf of an entire solenoid:

B=μ0NI/d emf = |d(mag flux)/dt| = d/dt|μ0NI/d(piR^2)| = μ0NI/d(piR^2)dI/dt emf = N(μ0N/d(piR^2)dI/dt)= (μ0N^2/d(piR^2)dI/dt)

Middling

What is the self inductance of a common solenoid?

-The self inductance is the constant in the inductance formula solved above. This means that the self inductance constant for a solenoid is (μ0N/d(piR^2)

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