#4 In the figure below you see a solenoid which has radius R, height h, N number of turns , and n number of turnsper unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field tobe uniform inside the solenoid and zero outside it, when a current I is flowing through the coils.RIh1. Calculate B, the magnitude of the magnetic field produced by I inside the solenoid.2. Calculate u B , the magnetic energy density inside the solenoid.3. Integrate the magnetic energy density in the volume to obtain UB, the magnetic energy stored in the solenoid.4. The energy stored in an inductor of self-inductance L can also be expressed as UB= ;LI² .Use the result ofpart 3 to calculate the self- inductance of the solenoid.

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In the figure below you see a solenoid which has radius R, height h, N number of turns , and n number of turns per unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field to be uniform inside the solenoid and zero outside it, when a current I is flowing through the coils.

In the figure below you see a solenoid which has radius R, height h, N number of turns , and n number of turns per unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field to be uniform inside the solenoid and zero outside it, when a current I is flowing through the coils.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter31: Inductance

Section: Chapter Questions

Problem 6P: A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

In the figure below you see a solenoid which has radius R, height h, N number of turns , and n number of turns
per unit length. Consider its height to be much larger than its radius, so that we can assume the magnetic field to
be uniform inside the solenoid and zero outside it, when a current I is flowing through the coils.
R
I
h
1. Calculate B, the magnitude of the magnetic field produced by I inside the solenoid.
2. Calculate u B , the magnetic energy density inside the solenoid.
3. Integrate the magnetic energy density in the volume to obtain UB, the magnetic energy stored in the solenoid.
4. The energy stored in an inductor of self-inductance L can also be expressed as UB= ;LI² .Use the result of
part 3 to calculate the self- inductance of the solenoid.

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