A solenod of length 0.4m and diametre 0.6m consists of a single layer of 1000 turns of fine wire carrying a current of `5.0xx10^-3A` . Calculate the magnetic field intensity on the axis at the middle and at the ends of the solenoid.

Explanation

`B=(1)/(2)mu_(0)ni[costheta_(1)-costheta_(2)]`
`impliesn=(1000)/(0.4)=2500` per under
`i=5xx10^(-3)A`
(i)
`costheta_(1)=(0.2)/(sqrt((0.3)^(2)+(0.2)^(2)))=(0.2)/(sqrt(0.13))`
`costheta_(2)=(-0.2)/(sqrt(0.3))`
`impliesB=(1)/(2)xx(4xxpixx10^(-7))xx2500xx5xx10^(-3)(2xx0.2)/(sqrt(0.13))`
`=(pixx10^(-5))/(sqrt(13))T`
(ii)
At the end
`costheta_(1)=(0.4)/(sqrt((0.3)^(2)+(0.4)^(2)))=0.8`
`costheta_(2)=cos90^(@)=0`
`B=(1)/(2)xx(4xxpixx10^(-7))xx2500xx5xx10^(-3)xx0.8`
`implies B=2pixx10^(-6)Wb//m^(2)`