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(a)
Derivation of the magnetic fields :
Let us consider,
be the number of turns per unit length.
Consider a rectangular Amperian loop abcd. Along cd, the field is zero since the magnetic field is weak outside. Along bc and ad, the field component is zero.
for L=h
The total number of turn is
,
The enclosed current is ,
we know, from Ampere's circuit law,
(b) The toroid does not behave like a bar magnet and has no fringe effect and as well as it is circular while the solenoid behaves like a bar magnet, has the fringe effect and it is straight in nature.