Q.

The percentage increase in the magnetic field B when the space within a current carrying toroid is filled with aluminium, with a susceptibility  of 2.1×10-5, is 2.1 × 10-p. Find p.

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answer is 3.0.

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Detailed Solution

In the absence of aluminium the magnetic field is  B0=μ0H.As the space inside the toroid is filled with aluminium the field becomes B=μH=μ0(1+χ)HThe increase in the field is  B-B0=μ0χHThe percentage increase is  B-B0B×100=μ0χHμ0H×100 =  χ×100=2.1×10-3 ∵χ=2.1×10-5By comparison, p=3
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The percentage increase in the magnetic field B when the space within a current carrying toroid is filled with aluminium, with a susceptibility  of 2.1×10-5, is 2.1 × 10-p. Find p.