I got 1.50 x 10 -3 but it isn\'t correct. Can you explain please? A solenoid is

Question

I got 1.50 x 10-3 but it isn't correct. Can you explain please?

A solenoid is formed by winding 26.9 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 6.07 x10-3 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.) I got 1.50 x 10-3 but it isn't correct. Can you explain please?

Explanation / Answer

resistance R = rho*L/A = (1.59e-8*

I = v/R = V*A/rho*L

I = (V*pi*r^2) / (rho*L) .......... (1)

L = N*2*pi*r

N/L = 1/(2*pi*r)

B = uo*(N/L)*I

B = (uo*V*pi*r^2)/(2*pi*r*rho*L)

B = (uo*v*pi*r)/(2*pi*rho*L)

B = (uo*v*r)/(2*rho*L)

r = (B*2*rho*L)/(uo*v)

r = (6.07e-3*2*1.59e-8*26.9)/(4*3.14e-7*3.06)

r = 1.35*10^-3 m   <<<<<-------------answer

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