A solenoid is formed by winding 26.7 m of insulated silver wire around a hollow

Question

A solenoid is formed by winding 26.7 m of insulated silver wire around a hollow cylinder. The turns are wound as closely as possible without overlapping, and the insulating coat on the wire is negligibly thin. When the solenoid is connected to an ideal (no internal resistance) 3.06-V battery, the magnitude of the magnetic field inside the solenoid is found to be 6.49 10-3 T. Determine the radius of the wire. (Hint: Because the solenoid is closely coiled, the number of turns per unit length depends on the radius of the wire.)
m

Please provide explanation and answer.

Explanation / Answer

The resistance of the wire R = L / r^2    resistivity of silver = 1.59*10^-8 m    current I = V / R                    = V /   L / r^2                     = V*r^2 / L the number of turns per unit length first calculate the length of wire per turn = 2R   So the number of turns = L / (2 R* 2r) R is radius of solenoid   , r = radius of the wire the number of turns per length = 1 / (2R*2r) Magnetic field B = _0 n I    B = µo/(4R*r) * (V**r^2) / L   radius of the wire r   = 4R L*B / µoV              substitute the above values to get solution

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