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(a) A toroidal solenoid with an ain core has an average radlines of 0.15m, area of cross section 12 xx 10^(-4) m^(2) and 1200 turns. Obtain the self inductance of the foroid. Ignore field variation across the cross section of the foroid. (b) A second coil of 300 turns is wound closely on the toroid above. If the current in the primary coil is increased from zero to 2.0 A in 0.05 s, obruin the induced emſ in the secondary coil. |
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Answer» SOLUTION :(a) `B=mu_(0)n_(1)I=(mu_(0)N_(1)I)/(l)=(mu_(0)N_(1)I)/(2pi r)` TOTAL magnetic flux, `phi_(B)=N_(1)BA=(mu_(0)N_(1)^(2)IA)/(2pi r)` But `phi_(B)=LI"":. L=(mu_(0)N_(1)^(2)IA)/(2pi r)` `L=(4pi xx 10^(-7) xx 1200 xx 1200 xx 12 xx 10^(-4))/(2pi xx 0.15)H` `=2.3 xx 10^(-3)H=2.3` mH (b) `|e|=(d)/(dt)(phi_(2))`, where `phi_(2)` is the total magnetic flux linked with the second coil. `|e|=(d)/(dt)(N_(2)BA)=(d)/(dt)[N_(2)(mu_(0)N_(1)I)/(2pi r)A]` or `|e|=(mu_(0)N_(1)N_(2)A)/(2pi r)(dI)/(dt)` or `|e|=(2 xx 10^(-7) xx 1200 xx 300 xx 12 xx 10^(-4) xx 2)/(2 xx 0.15 xx 0.05)V` = 0.023V |
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