A closely wound solenoid 80 cm long has 5 layers of windings of 400 terns each. The diameter of the solenoid is 1.8 cm. It the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

Explanation

Given, length of the solenoid, `l = 80 cm = 0.8 m`
Total number of turns, ` N = 5 xx 400 = 2,000`
` :. ` Number of turns per unit length
` n = N/l = (2,000)/(0.8) = 2,500`
Diameter of solenoid , `D = 1.8` cm
Current flowing through the solenoid, `I = 8.0` A
` :. ` The magnitude of magnetic field inside the near its centre is given by
` B = mu_(0) n I`
` = 4 pi xx 10^(-7) xx 2,500 xx 8`
` = 2.5 xx 10^(2) T`
The direction of magnetic field is along the axis of solenoid.