A solenoid is designed to produce a magnetic field of 0.220 T at its center. It

Question

A solenoid is designed to produce a magnetic field of 0.220 T at its center. It has radius 4.00 cm and length 100.0 cm, and the wire can carry a maximum currentof 8.0 A. (a) What minimum number of turns per unitlength must the solenoid have?
1 turns/m

(b) What total length of wire is required?
2 m (a) What minimum number of turns per unitlength must the solenoid have?
1 turns/m

(b) What total length of wire is required?
2 m

Explanation / Answer

a) The magnetic field at the center of the solenoid is               B = o (N/L) i               0.220    = 4 x 10-7 * (N/1)* 8.0                ==> N/L = 21895 turns / m    b)    L = 100cm = 1 m    The number of turns N =21895 * L = 21895 * 1 = 21895 turns Each coil has radius = 0.04 m then    the length of each coil = 2 r = 2* 3.14 * 0.04 = 0.2512 m The total length of the wire required is       = N * 2 r = 21895 * 0.2512 = 5500 m

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