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A long straight wire is arranged along t...

A long straight wire is arranged along the symmetry axis of a toroidal coil of rectangular cross-section, whose dimensions are given in the figure. The number of turms on the coil is `N`, and permeability of the surrounding medium is unity. Fine the amplitude of the emf induced in this coil, if the current `i=i_(m) cos omegat` flows along the straight wire.

Text Solution

Verified by Experts

The correct Answer is:
`(mu_(0)homegai_(m)N)/(2pi) lnb/a`

Flux through each loop `phi=int_(a)^(b) Bdx=int_(a)^(b)mu_(0)/2I/x hdx`
`=mu_(0)/2Ih lnb/a`
`e=-N(dphi)/(dt)=-Nd/(dt)(mu_(0)/zhlnb/a)I`
`=-(Nmu_(0)h)/2lnb/ad(dt)i_(m)cosomegat`
`=(Nmu_(0)h)/2lnb/ai_(m)omegasinomegat`
`=(Nmu_(0)homegai_(m))/2 ln b/a sinomegat`
`e_(0)=(Nmu_(0)homegai_(m))/2 ln b/a`
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