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

Given:


Length of solenoid, L = 80cm


Number of turns = number of layers × number of turns per layer


Number of turns, n = 5 × 400 = 2000


Radius of solenoid, r = Diameter/2 = 0.9 cm


Current through the solenoid = 8.0A


We know that, magnetic field strength near the centre of solenoid is given by,


…(1)


Where,


B = Magnetic field strength


n = total number of turns


I = current through the coil


�0 is the permeability of free space.


�0 = 4 × π × 10-7 TmA-1


r = radius of coil


Now, by plugging the values In equation (1), we get,



⇒ |B| = 2.512 × 10-2T


Hence the magnetic field strength at the centre of the solenoid is 2.512 × 10-2T.


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