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For a toroid N = 500, radius = 40 cm, an...

For a toroid N = 500, radius = 40 cm, and area of cross section `=10cm^(2)`. Find inductance

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(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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