The solenoid has length L, diameter D, and n turns per unit length with each carrying current .<a href="void(0);%22"></a>It is usual to assume that thecomponent of the current along the z axisis negligible.(This may be assured by winding two layers of closely spaced wiresthat spiral in opposite directions.)From symmetry considerations it is possible to show that farfrom the ends of the solenoid, the magnetic field isaxial. <img height="260" alt="SolenoidZ.JPG" src="//img.wizedu.com/questions/8efcbce0-ccdb-11ec-be5a-8d5485e9fb36.JPG" width="320"/>Which figure shows the loop that the must beused as the Ampèrean loop for finding Bz(r) for r inside the solenoid?<img height="260" src="//img.wizedu.com/questions/8fd4df70-ccdb-11ec-b624-550417971881.JPG" width="320" alt=""/>b) Find Bz(r), the z component of themagnetic field insidethe solenoid where Ampère's law applies. c) The magnetic field inside a solenoid can befound exactly using Ampère's law only if thesolenoid is infinitely long. Otherwise, the Biot-Savart lawmust beused to find an exact answer. In practice, the field can bedetermined with very little error by using Ampère's law, aslong as certain conditions holdthat make the field similar to thatin an infinitely long solenoid. Which of the following conditions must hold to allow you to useAmpère's law to find a good approximation?<ol type="a" class=" list-paddingleft-2"><li>Consider only locations where the distance from the ends is many times D.</li><li>Consider any location inside the solenoid, as long as L ismuch larger than D for the solenoid.</li><li>Consider only locations along the axis of the solenoid.</li></ol>

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In: Physics

Magnetic Field inside a Very Long Solenoid

The solenoid has length L, diameter D, and n turns per unit length with each carrying current .It is usual to assume that thecomponent of the current along the z axisis negligible.(This may be assured by winding two layers of closely spaced wiresthat spiral in opposite directions.)From symmetry considerations it is possible to show that farfrom the ends of the solenoid, the magnetic field isaxial.

Which figure shows the loop that the must beused as the Ampèrean loop for finding B_z(r) for r inside the solenoid?

b) Find B_z(r), the z component of themagnetic field insidethe solenoid where Ampère's law applies.

c) The magnetic field inside a solenoid can befound exactly using Ampère's law only if thesolenoid is infinitely long. Otherwise, the Biot-Savart lawmust beused to find an exact answer. In practice, the field can bedetermined with very little error by using Ampère's law, aslong as certain conditions holdthat make the field similar to thatin an infinitely long solenoid.

Which of the following conditions must hold to allow you to useAmpère's law to find a good approximation?

Consider only locations where the distance from the ends is many times D.
Consider any location inside the solenoid, as long as L ismuch larger than D for the solenoid.
Consider only locations along the axis of the solenoid.

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genius_generous answered 2 years ago

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