Magnetic Field of a Solenoid

Created by ramin8 !!

A Solenoid is a type of electromagnet, which consists of a coil tightly wound into a helix. Usually it produces a uniform magnetic field when an electric current is run through it. The purpose of a solenoid is to create a controlled magnetic field.

The Main Idea

The purpose of this application is to explore another way to apply the Biot-Sarvart law. The magnetic field is uniform along the axis of the solenoid, when electric current is run through it. The solenoid has has to have coils much larger than the radius.

A Mathematical Model

This is the formula for the magnetic field inside a long solenoid: [math]\displaystyle{ B = {\mu _{0}} \frac{NI}{L} }[/math] This formula is used inside a long solenoid, when the radius of the solenoid is much smaller than the length. B is the magnetic field. [math]\displaystyle{ {\mu _{0}} }[/math] is a constant. N is the number of loops in the solenoid. L is the length of the solenoid.

To determine the direction of the magnetic field: use your right hand and curl your fingers towards the direction of the current and the direction that your thumb is pointing to is the direction of the magnetic field.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Simple

A simple example of this

Difficult

To solve for the magnetic field of a solenoid, you can use a four step process.

Step 1: Cut up the distribution into pieces and Draw the |Delta|B Think about this: a solenoid the length of L that's made up for N circular loops tightly wound, each with a radius of R and a conventional current in the loops is I.

We want to find the magnetic field contributed by each of the loops at any location along the axis of the solenoid.

Step 2: Write an Equation for the Magnetic Field Because of One Piece. The origin is located at the center of the solenoid. We find the integration variable x, which is given by the location of a single piece. d-x is given by the distance from the loop to the observation location. We also have to consider the number of loops

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

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See also

Solenoid Applications

Ampere's Law

Right Hand Rule

Magnetic Field of a Loop

Further reading

Books, Articles or other print media on this topic

External links

[1]

References

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