A closely wound solenoid `80cm` long has layers of windings of `400 turns` each. The diameter of the solenoid is `1*8cm`. If the current carried is `8*0A` estimate the magnitude of `vecB` inside the solenoid near its centre.

Explanation

Length of the solenoid `I=80cm=0.8m`
There are five layers of windings of 400 turns each on the solenoid.
`:.` Total number of turns on the solenoid, `N=5xx400=2000`
Diameter of the solenoid `D=1.8cm=0.018m`
Current carried by the solenoid `I=8.0A`
Magnitude of the magnetic field inside the solenoid near is centre is given by the relation `B=(mu_(0)NI)/1`
Where
`mu_(0)=` Permeability of free space `=4pixx10^(-7)TmA^(-1)`
`B=(4pixx10^(-7)xx2000xx8)/0.8=8pixx10^(-3)=2.512xx10^(-2)T`
Hence, the magnitude of the magnetic field inside the solenoid near its centre is `2.512xx10^(-3)T`