Example 5.9. Find the magnetic field of a very long solenoid, consisting of closely wound turns per unit length on a cylinder of radius R, each carrying a steady current I (Fig. 5.34). [The point of making the windings so close is that one can then pretend each turn is circular. If this troubles you (after all, there is a net current I in the direction of the solenoid's axis, no matter how tight the
Example 5.9. Find the magnetic field of a very long solenoid, consisting of closely wound turns per unit length on a cylinder of radius R, each carrying a steady current I (Fig. 5.34). [The point of making the windings so close is that one can then pretend each turn is circular. If this troubles you (after all, there is a net current I in the direction of the solenoid's axis, no matter how tight the
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![Example 5.9. Find the magnetic field of a very long solenoid, consisting of n
closely wound turns per unit length on a cylinder of radius R, each carrying a
steady current I (Fig. 5.34). [The point of making the windings so close is that
one can then pretend each turn is circular. If this troubles you (after all, there is
a net current in the direction of the solenoid's axis, no matter how tight the
Chapter 5 Magnetostatics
K
FIGURE 5.34
winding), picture instead a sheet of aluminum foil wrapped around the cylin-
der, carrying the equivalent uniform surface current K = n1 (Fig. 5.35). Or make
a double winding, going up to one end and then always in the same sense-
going back down again, thereby eliminating the net longitudinal current. But, in
truth, this is all unnecessary fastidiousness, for the field inside a solenoid is huge
(relatively speaking), and the field of the longitudinal current is at most a tiny
refinement.]
FIGURE 5.35](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48f160c5-0383-4908-ae1e-19315a03f968%2F90e04c0e-a325-484d-85a9-bdf6a055d6a8%2F1ytqtkd_processed.png&w=3840&q=75)
Transcribed Image Text:Example 5.9. Find the magnetic field of a very long solenoid, consisting of n
closely wound turns per unit length on a cylinder of radius R, each carrying a
steady current I (Fig. 5.34). [The point of making the windings so close is that
one can then pretend each turn is circular. If this troubles you (after all, there is
a net current in the direction of the solenoid's axis, no matter how tight the
Chapter 5 Magnetostatics
K
FIGURE 5.34
winding), picture instead a sheet of aluminum foil wrapped around the cylin-
der, carrying the equivalent uniform surface current K = n1 (Fig. 5.35). Or make
a double winding, going up to one end and then always in the same sense-
going back down again, thereby eliminating the net longitudinal current. But, in
truth, this is all unnecessary fastidiousness, for the field inside a solenoid is huge
(relatively speaking), and the field of the longitudinal current is at most a tiny
refinement.]
FIGURE 5.35
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