A solenoid of radius and total turns has length such that
PHYSICS · Subjective · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A solenoid of radius R and total turns N has length L such that L≫R.
(a) Show that at a point on the axis and well inside the solenoid, the magnetic field is approximately uniform and independent of the axial position.
(b) Derive an expression for the axial magnetic field at a point a distance x from one end of the finite solenoid (do not assume x≫R). Treat the winding as a series of circular current loops and use suitable approximations.
(c) Using the result of part (b), demonstrate mathematically that when L→∞, the expression reduces to the standard form for an ideal solenoid.
(d) Explain qualitatively why the field near the ends (fringing region) is weaker than the field at the centre.