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Question:

(a) State Ampere's circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius r having 'n' turns per unit length and carrying a steady current I. (b) An observer to the left of a solenoid of N terms each of cross section area A observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m=NIA

Solution:

(a)According to Ampere's circuital law, the line integral of magnetic field induction along a closed curve is equal to the total current passing through the surface enclosed in the closed curve times the permeability of the medium.∮B⋅dl=μ₀IenclosedApplying ampere's law for the given toroid,B(2πr)=μ₀NIBut,N=2πrnB=μ₀nI(b)The observer sees south pole as shown in the attached figure.Magnetic moment due to a loop is given by:m=iAFor N turns,i=NIm=NIA