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Find the percent increase in the magneti...

Find the percent increase in the magnetic field `B` when the space within a current- carrying toroid is filled with aluminium. The susceptibility of aluminium is `2.1 xx 10^(-5)`.

Text Solution

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Data: `X_(m) = 2.1 xx 10^(-5)`, positive, since aluminium is paramagnetic,
Let B and `B_(0)` be the magnetic inductions inside a toroid with and without aluminium core. Then,
`B_(0) = mu_(0)H` and `B=mu_(0)(1+X_(m))H`
Where H`-=` magnetic field strength and `mu_(0)` = Permeability of free space.
The percentage increase in the magnetic induction within the toroid due to the aluminium core
`=(DeltaB)/(B_(0)) xx 100 = (B-B_(0))/(B_(0)) xx 100 = (mu_(0)X_(m)H)/(mu_(0)H) xx 100 = X_(m) xx 100`
`=(2.1 xx 10^(-5)) xx 100 = 2.1 xx 10^(-3)` %
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