# A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical non-magnetic frame so that the successive turns nearly touch each other. What would be the magnetic field B at the center of the solenoid if it carries a current of 5A?

Given:

Radius of cylinder(r) = 0.5 mm = 5 x 10-4 m

Current(i) = 5 A

Formula used:

Magnetic field inside a long solenoid B = μ0ni,

where

μ0 = magnetic permeability of vacuum = 4π x 10-7 T m A-1, n = number of turns per unit length, i = current carried by the wire

Now, width of each turn = diameter of the wire = (0.5 x 2) mm = 1 mm = 10-3 m.

Hence, number of turns per unit length(n) (per m) =103 = 1000

Therefore, substituting the values:

B (magnetic field at the center) = 4π x 10-7 x 1000 x 5 T

= 6.28 x 10-3 T (Ans)

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