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?

Options

A. `6xx10^(3)m`
B. `1.2xx10^(2)m`
C. `4.8xx10^(2)m`
D. `2.4xx10^(3)m`

Answer

D

Explanation

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