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The magnetic flux passing through a metal ring varies with time `t` as: `phi_(B)=3(at^3-bt^2)T-m^2` with `a=2.00s^-3` and `b=6.00s^-2`. The resistance of the ring is `3.0Omega`. Determine the maximum current induced in the ring during te interval from `t=0` to `t=2.0s`. |
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Answer» Given `phi_B=3(at^3-bt^2)` `:. |e|=|(dphi_B)/(dt)|=9at^2-6bt` `:.` Induced current, `i=(|e|)/R=(9at^2-6bt)/3=3at^2-2bt` For cuurrent to be maximum, `(di)/(dt)=0` `:. 6at-2b=0` or `t=b/(3a)` i.e. at `t=b/(3a)`, current is maximum. This maximum current is `i_max.=3a(b/(3a))^2-2b(b/(3a))` `= b^2/(3a)-(2b^2)/(3a)=b^2/(3a)` Substituting the given values of `a` and `b` we have `i_max=((6)^2)/(3(2))=6.0A` |
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