A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (a) What minimum number of turns per unit length must the solenoid have? (b) What total length of wire is required?

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Part (a)The expression for the magnetic field at the center of the solenoid,B=μ0NIL Rearranging the equation,NL=Bμ0In=Bμ0IStep 2Substitute,n=0.0270 T4π×10-7 T-m/A12.0 A=1790 turns/m Therefore, the minimum number of turns per unit length in the solenoid is 1790 turns/m.Part (b)The total number of turns in the solenoid,N=nL Substitute,N=1790 turns/m40×10-2 m=716 turnsStep 4The total length of the wire,Ltotal=N2πR Substitute,Ltotal=716 turns2π1.40×10-2 m=63.0 m Therefore, the total length of the required wire is 63.0 m. ...