A magnetic field of 0.113 T exists in the region enclosed by a solenoid that has

Question

A magnetic field of 0.113 T exists in the region enclosed by a solenoid that has 274 turns and a diameter of 7.72 cm. Within what period of time must the field be reduced to zero if the average magnitude of the induced emf within the coil during this time interval is to be 9.94 kV? Answer in units of s A two-turn circular wire loop of radius 0.514 in lies in a plane perpendicular to a uniform magnetic field of magnitude 0.314 T. If the entire wire is reshaped from a two- turn circle to a one-turn circle in 0.15 s (while remaining in the same plane), what is the magnitude of the average induced emf E in the wire during this time? Use Faraday's law in the form E = Delta(N Phi)/Delta t. Answer in units of V

Explanation / Answer

1.

Area of solenoid

A=pi*d2/4 =pi*0.07722/4

A=4.681*10-3m2

Induced emf

E=NBA/t

=>t =NBA/E =274*0.113*4.681*10-3/(9.94*103)

t=1.458*10-5s

2.

Number of turns

N=L/2pir

=>L=N*2pir =2*2pi*0.514

L=6.46 m

Area of Circular loop

A=pi*r2=pi*0.5142=0.83 m2

Total area of 2 circular loops

A1=2*0.83=1.66 m2

radius of single loop circle

r=L/2pi =6.46/2pi =1.028 m

A2=pi*1.0282=3.32m2

Initial Flux

X=phi

X1=BA1 =0.52124 Wb

Final Flux

X2=BA2 =1.04248

Induced emf

E=-N(dX/dt) =1*(1.04248-0.52124)/0.15

E=-3.475 Volts

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