(a) Derive, with the help of a diagram, the expression for the magnetic field inside a very long solenoid having n turns per unit length carrying a current I.
(b) How is a toroid different from a solenoid?
(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,
This is the derived expression for the magnetic field.
(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.