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The magnetic field inside a long solenoi...

The magnetic field inside a long solenoid having 50 turns `cm^(-1)` is increased from `2.5 xx 10^(-3) T` to `2.5 T` when an iron core of cross-sectional area `4 cm^2` is inserted into it. Find `(a)` the current in the solenoid, (b) the magnetization `I` of the core and (c) the pole strength developed in the core.

Text Solution

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Here `B_1=2.5xx10^(-3)T`
`B_2=2.5 T`
`A=4xx10^(-4)m^2,`
`n=50 turns//cm `
`=5000turns//m`
`(a) 2.5xx10^(-3)=4 pi xx10^(-7) xx5000xxi`
`implies i=(2.5xx10^(-3))/(4 pixx 10^(-7)xx5000)`
`=0.398A=0.4 A`
`(b) I=(B_2)/(mu_0)H`
`=(2.5xx10^(-3))/(4 pi xx10^(-7)).(B_2-B_1)`
`=(2.5xx2.5(1-(1)/(1000)))/(4 pixx10^(-7))`
`~~2xx0^6 A//m`
`(c) i=M/V`
` l=(MI)/(AI)=m/A`
`m=lA`
`=2xx10^(6)xx4xx19=0^(-4)`
`=800 A-m`.
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