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 center.

Explanation

Length of the solenoid, `l = 80 cm = 0.8 m`
There are five layers of windings of 400 turns each on the solenoid.
`:.` Total number of turns on the solenoid, `N = 5 xx 400 = 2000`
Diameter of the solenoid, `D = 1.8 cm = 0.018 cm`
Current carried by the solenoid, `I = 8.0A`
Magnitude of the magnetic field inside the solenoid near its centre is given by relation,
`B = (mu_(0)NI)/(l)`
Where,
`mu_(0) =` Permeability of free space `= 4n xx 10^(-7) T mA^(-1)`
`B = (4pi xx 10^(-7) xx 200 xx 8)/(0.8)`
`= 8pi xx 10^(-3) = 2.512 xx 10^(-2)T`
Hence, the magnitude of the magnetic field inside the solenoid near its centre is `2.512 xx 10^(-2)T`.