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Field of a Solenoid

# Field of a Solenoid - P on the axis of the solenoid The...

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Field of a Solenoid In many instances a wire is coiled in a helical pattern to create a cylindrically shaped object known as a solenoid. These objects are frequently used in magnetic experiments, as they create an almost uniform field inside the cylinder. The solenoid can be seen as the superposition of a large number of rings, one on top of the other. Shown below is a typical solenoid, with its field lines: Figure %: A solenoid, shown with some field lines The field has a similar shape as a ring, but appears more "stretched", a result of the cylindrical shape of the object. We can use the same method to find the magnitude of the magnetic field on the axis of the solenoid that we did with the ring. However, the calculus is long and complicated and, since we have already gone through the process, we will simply state the equations. Consider a solenoid with n turns per centimeter, carrying a current I , shown below.

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Figure %: The inside of a solenoid, shown with a point
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Unformatted text preview: P on the axis of the solenoid The field at point P is given by: B = (cos θ 1- cos θ 2 ) where θ 1 and θ 2 are the angles between vertical and the lines from P to the edge of the solenoid, as shown in the figure. Analyzing this equation we see that the longer the solenoid, the greater the magnitude of the magnetic field. From the above equation we can generate an expression for the field of a solenoid infinite in length. In an infinite solenoid there is a uniform magnetic field in the direction of the axis, given by: B = (cos 0 - cosΠ ) = This is the magnitude of the uniform field inside the solenoid. The field outside an infinite solenoid is always zero. The study of these complex wire shapes concludes our study of the sources of magnetic fields. In the next SparkNote in the series on magnetic forces and fields we will take a more theoretical approach to magnetism, describing some of the properties of all magnetic fields....
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