Solenoid Magnetic Field

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					Magnetic Field on the Axis of a Solenoid

 • Number of turns per unit length: n = N/L
 • Current circulating in ring of width dx′ : nIdx′
                                        µ0 (nIdx′ )           R2
 • Magnetic field on axis of ring: dBx =
                                             2      [(x − x′ )2 + R2 ]3/2
 • Magnetic field on axis of solenoid:
                                                                                                       !
       µ0 nI 2
                 Z   x2           dx′                 µ0 nI       x − x1            x − x2
Bx =        R                                     =           p                −p
         2       x1       [(x − x′ )2 + R2 ]3/2         2      (x − x1 )2 + R2   (x − x2 )2 + R2




                                                                                           26/3/2008   [tsl215 – 3/16

				
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