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A winding wire which is used to prepare ...

A winding wire which is used to prepare a solenoid of length 80 cm can bear a maximum cuurent of 10 A. the cross-sectional radius of the solenoid is 3 cm. what should be the length of the winding wire if a magnetiic field of 0.2 T is to be produced at the centre of the solenoid along its axis?

A

`6xx10^(3)m`

B

`1.2xx10^(2)m`

C

`4.8xx10^(2)m`

D

`2.4xx10^(3)m`

Text Solution

Verified by Experts

The correct Answer is:
D
Magnetic field inside a solenoid
is `B=mu_(0)ni=(mu_(0)Ni)/(l)thereforeN=(Bl)/(mu_(0)i)`
where N=total number of turns
`thereforeN=(0.2xx0.8)/(4pix10^(-7)xx10)`
`=(4xx10^(4))/(pi)`
`theefore`Since there are N turns each of length `l=2pir`
`thereforeL=Nxx2pir`
`=(4xx10^(4))/(pi)xx2pixx3xx10^(-2)`
`=2.4xx10^(3)`m
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Knowledge Check

  • A winding wire which is used to frame a solenoid can bear a maximum 10 A. current If length of solenoid is 80 cm and its corss sectional raedius is 3 cm , then required length of winding wire is (B =0.2T)

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    `2.4 xx10^(3) m`
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    `6xx 10^(3) m`

  • A solenoid of length 20cm and radius 2cm is closely wound with 200 turns. The magnetic field intensity at either end of the solenoid when the current in the winding is 5 amp . Is

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    `2500Amp//m`
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    `1750 Amp//m`
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