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The core of a toroid having 3000 turns h...

The core of a toroid having 3000 turns has inner and outer radii of 16 cm and 17 cm respectively . The magnetic field in the core for a current of `0.07` A is 2.5 T . What is relative permeability of the core ?

Text Solution

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`B = mu _(0) u_(i) ni`
`= mu _(0) u _(r) (N)/(epir ) xxi`
`= (mu_(0))/( 4pi) mu_(r) xx (2Ni)/(r )`
`= 2.5 = 10 ^(-7) xx mu _(r ) xx (2xx 3000 xx 0.07)/((33)/(2) xx 10 ^(-2))`
`=rarr 2.5 = (10 ^(-7) xx 4 xx 3 xx 7 xx 10 ^(3) xx mu _(r))/(33)`
`implies 27.5 = 28xx 10^(-4) xx mu_(r)`
` implies mu_(r) = (27.5)/(28) xx 10 ^(4)`
` = 0.9821429 xx 10 ^(4)`
`therefore mu _(r) = 9821`
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