Solve Solenoid Resistance/Magnetic Field/Length

[Chocobo7]

It is desired to construct a solenoid that has a resistance of 9.29 ohm and produces a magnetic field at its center of 0.0642 T when it carries a current of 7.32 A. The solenoid is to be constructed from copper wire having a diameter 0.895 mm.
The resistivity of the copper is 1.7x10-8 ohm-m.
Find the # of turns of wire needed if the radius of the solenoid is to be 1.26 cm. Answer in units of turns.
Find the length of the solenoid. Answer in units of cm.

This is what I did:
B=N x muI/2R
.0642=N x (4pi x 10-7)(7.32)/(2*.0126)
N=175.879 turns
...But this is wrong. Can you please help me out & let me know what I did wrong?

Find the length of the solenoid. Answer in units of cm.
I used:
R=pl/A
9.29=1.7x10-8(l)/(.000895/2)^2 *pi
l=34379.8 cm
...I think this one is wrong too. Any help would be appreciated! Thanks in advance!

 

[Chocobo7]

nevermind. thanks anyway

 

[kyle8921]

I would like to clarify that the formula B=N x muI/2R is used for calculating the magnetic field strength at the center of a solenoid, not for finding the number of turns of wire needed. To find the number of turns of wire needed, we can use the formula N = (R x A)/(rho x L), where R is the desired resistance, A is the cross-sectional area of the wire, rho is the resistivity of the wire, and L is the length of the wire.

Using this formula, we can calculate the number of turns as N = (9.29 x (pi x (0.000895/2)^2))/(1.7x10^-8 x 0.0126) = 174.9 turns. This is close to the value you calculated, but the difference may be due to rounding off.

To find the length of the solenoid, we can use the formula L = (R x A)/(rho x N^2), where R is the desired resistance, A is the cross-sectional area of the wire, rho is the resistivity of the wire, and N is the number of turns.

Using this formula, we can calculate the length as L = (9.29 x (pi x (0.000895/2)^2))/(1.7x10^-8 x 174.9^2) = 0.0408 cm. This is significantly different from your calculation, which may be due to using the wrong formula or incorrect conversion of units.

In summary, to construct a solenoid with a resistance of 9.29 ohm and a magnetic field of 0.0642 T at its center, using copper wire with a diameter of 0.895 mm, we would need approximately 175 turns of wire and the length of the solenoid would be 0.0408 cm. I hope this helps clarify the calculations for you.