If the radius of the solenoid is to be 1.00 cm, determine the number of turns of wire needed.

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It is desired to construct a solenoid that will have a resistance of 4.30 Ω (at 20.0°C) and produce a magnetic field of 3.40 image 10-2 T at its center when it carries a current of 3.50 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.
 turns

(b) If the radius of the solenoid is to be 1.00 cm, determine the required length of the solenoid.
 cm 
asked Feb 26, 2012 in Physics by awesome ~Expert~ (1,479 points)
    

1 Answer

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Best answer

The resistance of a wire is given by:

R = p*L / A  (*where p=resistivity of material, L=length, A=area, R=resistance)

rearranging the equation we can solve for L, 

L = (R*A) / p

we are given R = 4.3 Ω

A = area of circle = pi*r^2 ,

r = radius =  diameter / 2  = 0.5 / 2  mm  = (0.5 / 2 )*10^-3 m = 0.25*10^-3 m

so A = pi*(0.25*10^-3 m)^2 

and p = resisitivity of copper, which is 1.7*10^-8 Ω*m

 (for a list of resisitivity of materials refer to this link:  http://answermenu.com/?qa=325/platinum-copper-equal-length-found-resistance-ratio-radii

 

plugging into formula above we can solve for L:

L = ( (4.3 Ω)*(pi*(0.25*10^-3 m)^2 )) / (1.7*10^-8 Ω*m )

L = 49.7 m

The total number of turns on the solenoid is given by:

N = L / (2pi*r)

plugging in our numbers we get:

r = 1 cm = 1*10^-2 m

N =49.7 m / (2pi*(1*10^-2 m))  = 790 turns

answered Feb 26, 2012 by pokemonmaster ~Expert~ (3,856 points)
selected Feb 26, 2012 by awesome
This doesn't equate to 3.4 0 * 10^-2 T?. B = mu * N * I/L

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