Magnetic Field of a Solenoid: Difference between revisions
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This is the formula for the magnetic field inside a long solenoid: | This is the formula for the magnetic field inside a long solenoid: | ||
<math> B = {\mu _{0}} \frac{NI}{L}</math> | <math> 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>{\mu _{0}}</math> is a constant. | |||
N is the number of loops in the solenoid. | |||
L is the length of the solenoid. | |||
===A Computational Model=== | ===A Computational Model=== | ||
| Line 24: | Line 28: | ||
Step 1: Cut up the distribution into pieces and Draw the |Delta|B | 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. | 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 | Step 2: Write an Equation for the Magnetic Field Because of One Piece. | ||
The origin is located at the center of the solenoid. | The origin is located at the center of the solenoid. | ||
We find the integration variable | |||
[[File:solenoid.jpg]] | [[File:solenoid.jpg]] | ||
===Simple=== | ===Simple=== | ||
A simple example of this | |||
===Middling=== | ===Middling=== | ||
===Difficult=== | ===Difficult=== | ||
Revision as of 11:38, 5 December 2015
Claimed 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.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
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
Simple
A simple example of this
Middling
Difficult
Connectedness
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History
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See also
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