14 May DETERMINE THE FIELD AT THE ENDS OF THE SOLENOID.
We calculated the magnetic field along the axis of a circular loop of wire
of radius a carrying a current I as a function of the distance x from the center.
(i) Use this result to derive the magnetic field along the axis of a cylindrical
solenoid with (finite) length L, radius a, and n turns of wire per unit length.
(ii) Determine the field at the ends of the solenoid.
(iii) Use a computer to plot the magnetic field strength as a function of the
position along the axis. Use L = 2.0m, a = 0.2m, n = 1000m−1, and I = 1 A.
(iv) Show that for L a the field near the center of the solenoid is nearly
constant and is nearly equal to the field inside an infinite solenoid.
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