Inductance

Made by Mackenzie Rideout

Short Description of Topic

The Main Idea

Inductance is intimately connected with Faraday’s law of electromagnetic induction. According to this law there is an induced electromotive force in any circuit whenever the magnetic flux linked with that circuit changes. A circuit carrying a current always has some linked magnetic flux due to that current. A change in the current leads to a change in the flux, and the change in flux in turn gives rise to an induced e.m.f. Furthermore, the induced e.m.f. is always in such a direction that it tends to oppose the change in current: there is a forward e.m.f. if the current is being reduced and a backward e.m.f. if it is being increased.

As seen in figure (A) the induced emf, due to a solenoid, in this case is in such a direction that opposes the change in current. In this case the induced emf acts like a battery placed backwards in comparison of the original one. This, reduces the rate at which the current is increasing.

The opposite happens in figure (B) the induced emf, due to a solenoid in this case, is in such direction that opposes the change in current. In this case the emf acts like a battery placed in the same direction as the original one. This, reduces the rate at which the current decreases.

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 . 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 the magnetic field in a solenoid

To understand the inductance lets go step by step through the examples and get the main formula for Inductance.

Examples

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

Simple

Emf of an entire solenoid:

Middling

What is the self inductance of a common solenoid?

Given a circuit consisting of a solenoid, a resistor and a emf, in which a current is changing, increasing in this example.

Recall that when there is a change in the magnetic flux, there is a emf produced. In this example, the generated emf due to the change in the magnetic flux generated by the change in the current, is what we will call the emf induced, since it is induced by the changing current in the solenoid.

To understand what is happening in the solenoid in a qualitative matter, lets take a look at the solenoid when there is a changing current.

As the current increases, the magnetic field generated by the solenoid increases. There is a Non Coulomb electric field generated by the changing magnetic field opposing the direction of the increasing magnetic field. In the picture, the Non Coulomb electric field (Enc) is in red. As stated, the Non Coulomb electric field polarizes the solenoid.

Given the polarization of the solenoid a new Electric field is created as seen in the above picture in yellow.

Therefore, the change in voltage of the solenoid is equal to the induced emf, that we just derived in previous steps and is named as equation (1). Assuming there is no resistance in the solenoid coil, the change in voltage for the solenoid equals the emf induced.

As you can see in equation (2) from the picture above, the term "L" is the inductance of the device, the inductor, in this case the solenoid.

Comparing equations (1) and (2) we derive the general formula for Inductance

Difficult

What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.

Now that we have derived the general formulas for inductance, we can solve this problem in the following manner,

Connectedness

1. This topic is interesting because solenoids are a very common placed tool. It is important to know how they operate in order to use them to the best of their capabilities.
2. This topic is personally connected to me because of my major. I am a mechanical engineer and am currently enrolled in ME2110, the "robot building class". In this class to assist with our designs, we often used solenoids as deployment mechanism. Being able to learn about this topic while working with the objects hands on in a non-physics environment helped me immensely in my design process and physics career.

History

The history of inductance goes back quite a long time ago and is pretty complicated. In the early 19th century there were actually two scientist discovering inductance in parallel with each other, one in America and one in England. These two scientist names are Joseph Henry and Michael Faraday. Because of this there is no one named founder of inductance, but both of them did receive credit. Inductance now finds itself as one of Faraday's Laws, giving Michael Faraday his due credit. While the units for inductance are "Henries" named after Joseph Henry.

See also

Faraday's Law

Further reading

Information for this page was found in Matter and Interactions Volume II. If you would like to know more about this topic or other topics like it, please reference this book.

Images

All images are property of one of the collaborators.

References

This section contains the the references you used while writing this page

[1] The Main Idea M S Smith 1967 Phys. Educ. 2 195