Abstract: For a steady current-carrying tightly wound solenoid with finite length, first, the expression of vector potential is derived by using the method of cylindrical function expansion and the expressions of magnetic field in the integral form are obtained by employing the relation between vector potential and magnetic induction. Next, the analytic expressions in the series form of magnetic field distribution are calculated by using the integration method directly. Finally, the magnetic field on some special positions is discussed.

Key words: solenoid, steady current, magnetic field, magnetic induction, series expression