You wish to construct a solenoid with a diameter of 2.00 cm that will produce a

Question

You wish to construct a solenoid with a diameter of 2.00 cm that will produce a magnetic field of 4.80 times 10^-2 T at its center when a current of 16.0 A is passing through the coils. You want the resistance of the coil wire to be 7.80 Ohm. The resistivity of the wire used is 1.70 times 10^-8 Ohm. m (at 20.0degreeC), and you are using a wire that has a cross sectional area of 3.14 times 10^-8 m^2. (Note that this solenoid may not necessarily be so tightly wound that the adjacent loops of wire will touch each other. Nonetheless, you may assume that it behaves like an ideal solenoid.) Determine the following. number of turns needed on the solenoid_______turns length of the solenoid_____m

Explanation / Answer

B = mu*N*I/L
r = 0.01 m
R = 7.8 ohm
rho = 1.7*10^-8
A =3.14*10^-8
R = rhoL/A
L = 14.407 m

length of solenoid = l
and 2*pi*r*N = L
N = 229.41 turns

4.8*10^-2 = 4*pi*10^-7*N*16/L
L = 9.60 cm

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