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An air cored solenoid is of length 0.3 m...

An air cored solenoid is of length 0.3 m, area of cross section `1.2 xx 10^(-3) m^(2)` and has 2500 turns. Around its central section, a coil of 350 turns is wound. The solenoid and the coil are electrically insulated from eachother. Calculate the e.m.f. induced in the coil if the initial current of 3 A in the solenoid is reversed in 0.25 s.

Text Solution

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`N_(1)=2500, " " N_(2)=350 " " A=1.2xx10^(-3)m^(2)`
`1=0.3m. " " dI=3-(-3)=3+3=6A " " dt=0.25s`
Since mutual inductance,
`M=(mu_(0)N_(1)N_(2)A)/(l)=(4pi xx10^(-7)xx2500xx350xx1.2xx10^(-3))/(0.3)`
`=(4xx3.14xx1.05xx10^(-4))/(0.3)=43.96xx10^(-4)=4.39xx10^(-3)H`
Induced emf `|E|=M(dI)/(dt)=(4.39xx10^(-3)xx6)/(0.25)=105.36xx10^(-3)=0.10536 V`.
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