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A copper wire having a resistance of 0*0...

A copper wire having a resistance of `0*015Omega` per metre is used to wind a `500` turns solenoid of radius `1*0cm` and length `22cm`. If the e.m.f. of the battery used is `6V`, then find the magnetic field near the centre of the solenoid.

Text Solution

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Resistance of wire per metre
`=0*015Omegam^-1`
No. of turns in solenoid, `N=500`,
radius, `r=1xx10^-2m`,
length of solenoid `L=22cm=22xx10^-2m`,
e.m.f., `epsilon=6V`
Length of wire used in solenoid
`l=2pirxxN=2xx22/7xx(1xx10^-2)xx500m`
`=31.4m`
Total resistance of wire used in solenoid,
`R=`resistance permetrexxl
`=0*015xx31.4Omega`
Current in solenoid,
`I=epsilon/R=(6)/(0*015xx31.4)=12.73A`
Magnetic field near the centre of solenoid
`B=mu_0(NI)/(L)=(4pixx10^-7)xx(500xx12.73)/((22xx10^-2))`
`=3*64xx10^-2T`
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