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

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  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

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

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 ~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