(a) Using Ampere's circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.
(b) In what respect is a toroid different from a solenoid ? Draw and copare the patern of the magnetic field lines in the two cases.
(c) How is the magnetic field inside a given solenoid made strong?

Explanation

(b) The toroid is a hollow circular ring on which a large number of turns of an insulated copper wire are closely wound. Thus, toroid can be viewed as a solenoid which has been bent into a circular shape to close on itself.
Magnetic field lines due to a solenoid and a toroid are given in fig. (a) and (b) respectivley.

Magnetic field inside a solenoid is uniform, strong and along the axis of solenoid and field lines are almost parallel lines. Magnetic field lines inside a toroid make a closed path.
(c ) Magnetic field inside a given solenoid be made strong by inserting a soft iron core inside the solenoid.