# (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.

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