You have a 0.600-m-long copper wire. You want to make an N-turn current loop that generates a 1.30 mT magnetic field at the center when the current is 0.600 A. You must use the entire wire.
What will be the diameter of your coil?
this doesnt seem that hard but I cant figure what I need to use.
The value of coil diameter D will depend upon the value of N. There will be only value of D possible with the length L that you have
B (at the center of the coil) = N*mu*I/D
"mu" = 4 pi*10^-7 Weber*Amp/meter
N = L/(pi*D) determines how many turns you can have with the available wire length L
B = [L/(pi*D)]*mu*I/D
= L*mu*I/(pi*D^2)
Solve for D
thanks i guess i need to read up on the turns in coils.
To find the diameter of the coil, we can use the formula for the magnetic field at the center of a current loop:
B = (μ₀ * N * I) / (2 * R)
where B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 T·m/A), N is the number of turns, I is the current, and R is the radius of the loop.
Since we want the magnetic field to be 1.30 mT, which is equivalent to 1.30 x 10^-3 T, and the current is 0.600 A, we can rearrange the equation to solve for R:
R = (μ₀ * N * I) / (2 * B)
Substituting the given values:
R = (4π x 10^-7 T·m/A * N * 0.600 A) / (2 * 1.30 x 10^-3 T)
Simplifying:
R = (2π * N * 0.600) / (1.30 x 10^-3)
Now, we know that the length of the wire is equal to the circumference (C) of the coil:
C = 2πR
Since the length of the wire is given as 0.600 m, we can solve for R:
0.600 = 2πR
Rearranging the equation to solve for R:
R = 0.600 / (2π)
Substituting the value of R back into the previous equation:
R = (2π * N * 0.600) / (1.30 x 10^-3)
0.600 / (2π) = (2π * N * 0.600) / (1.30 x 10^-3)
Simplifying:
N = (0.600 / (2π)) / ((2π * 0.600) / (1.30 x 10^-3))
Calculating:
N ≈ 109
Now that we have the number of turns, we can substitute it back into the equation for R:
R = (2π * N * 0.600) / (1.30 x 10^-3)
Calculating:
R ≈ 0.873 m
Finally, the diameter (D) of the coil is twice the radius:
D = 2R
D ≈ 2 * 0.873 m
Therefore, the diameter of the coil will be approximately 1.75 m.
To determine the diameter of the coil, you can use the formula for the magnetic field at the center of a current-carrying loop. The formula is given by:
B = (μ₀ * N * I) / (2 * R)
Where:
B is the magnetic field at the center of the loop,
μ₀ is the permeability of free space (constant),
N is the number of turns in the loop,
I is the current flowing through the loop, and
R is the radius of the loop.
In this case, you want the magnetic field (B) to be 1.30 mT (millitesla), the current (I) to be 0.600 A, and the length of the wire to be 0.600 m. To use the entire wire, the length of the wire (circumference) will be equal to the perimeter of the loop:
Perimeter = 2 * π * R
Since the length of the wire is given as 0.600 m, we can set up the equation:
0.600 m = 2 * π * R
Rearranging the equation, we can solve for R:
R = (0.600 m) / (2 * π)
Now, substitute the given values into the magnetic field equation and solve for N:
1.30 mT = (4π * 10^-7 T*m/A) * N * (0.600 A) / (2 * R)
Substituting the value of R from the previous equation:
1.30 mT = (4π * 10^-7 T*m/A) * N * (0.600 A) / (2 * (0.600 m) / (2 * π))
Simplifying, we get:
1.30 mT = (4π * 10^-7 T*m/A) * N * (0.600 A) / (0.600 m)
Now, you can solve this equation for N:
N = (1.30 mT * 0.600 m) / (4π * 10^-7 T*m/A * 0.600 A)
N ≈ 1.091 x 10^7 turns
Finally, substitute the value of N into the equation for the perimeter:
Perimeter = 2 * π * R
Perimeter ≈ 2 * π * (0.600 m) / (1.091 x 10^7 turns)
Now that you have the perimeter, you can calculate the diameter by dividing the perimeter by π:
Diameter ≈ Perimeter / π
Diameter ≈ (2 * π * (0.600 m) / (1.091 x 10^7 turns)) / π
Simplifying, we get:
Diameter ≈ 0.367 m
Therefore, the diameter of your coil will be approximately 0.367 meters.