A solenoid 10.0 cm in diameter and 70.6 cm long is made from copper wire of diam

Question

A solenoid 10.0 cm in diameter and 70.6 cm long is made from copper wire of diameter 0.100 cm, with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adjacent turns touching each other. What power must be delivered to the solenoid if it is to produce a field of 7.50 mT at its center? It is desired to construct a solenoid that will have a resistance of 4.60 ohm (at 20.0 degree C) and produce a magnetic field of 4.30 times 10^-2 T at its center when it carries a current of 4.70 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. (a) If the radius of the solenoid is to be 1.00 cm, determine the number of turns of wire needed. b) If the radius of the solenoid is to be 1.00 cm, determine the required length of the solenoid.

Explanation / Answer

n = 1000 turns/m

N = 1000*0.706 = 706 turns

B = mue0*ni

i = 7.5*10^-3/4*3.14*10^-7*1000 = 5.97 amp

L = N*pi*d = 70.6*pi m

R = rho*L/A = 1.7*10^-8*70.6pi/pi(0.05^2*10^-4) = 4.8 ohm

power p = i^2R = 171.08 W

10) R = rho*l/A

l = R*A/rho

l = 4.6*3.14*(0.25^2*10^-6)/1.7*10^-8 = 53.1 m

N = l/2pir = 846 turns

B = mue0*ni

n = 4.3*10^-2/4*3.14*10^-7*4.7 = 7284.2 turns/m

L = N/n = 0.116 m = 11.6 cm

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