1) A technician has been given wire that can safely carry 5 A. She has been instructed to construct a solenoid that will have a magnetic field of 0.06 T at its center. After completing some tests of the wire, the technician finds that the tightest safe winding possible with the wire will provide 10 loops/cm. Will the technician be able to construct the desired solenoid with this wire?
2) A technician operating a winding machine constructs a solenoid from 200 m of copper wire wound on a plastic base with a diameter of 5 cm. The base is 25 cm long. how much current must flow through the wire to provide a magnetic field of 0.15 T at the center of the solenoid? is this reasonable?
Thank you!
1) To determine if the technician can construct the desired solenoid, we need to calculate the number of turns required for the solenoid using the given information.
First, we convert the given value of 10 loops/cm to loops/meter. Since there are 100 cm in a meter, we multiply 10 loops/cm by 100 to get 1000 loops/m.
Next, we calculate the length of the solenoid needed. The length of the solenoid is not given in the question, so we assume it is 1 meter for simplicity.
Therefore, the number of turns required for the solenoid is 1000 turns/meter.
Now, we need to check if the wire can handle the required current. Given that the wire can safely carry 5 A, we need to check if the total current in the solenoid will exceed this limit.
The total current in the solenoid is calculated by multiplying the number of turns by the current per turn. In this case, the current per turn is not given, so we assume it to be 1 A for simplicity.
Therefore, the total current in the solenoid is 1000 turns/meter * 1 A/turn = 1000 A.
Since the total current in the solenoid exceeds the safe limit of 5 A, the technician will not be able to construct the desired solenoid with this wire.
2) To determine the current required to achieve a magnetic field of 0.15 T at the center of the solenoid, we need to use the formulas for the magnetic field and solenoid characteristics.
The formula for the magnetic field inside a solenoid is given by:
B = μ₀ * n * I
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^⁻7 T m/A), n is the number of turns per unit length (turns/m), and I is the current flowing through the solenoid (A).
We can rearrange the formula to isolate the current (I):
I = B / (μ₀ * n)
Given the values:
B = 0.15 T (the desired magnetic field)
μ₀ = 4π × 10^⁻7 T m/A (permeability of free space)
n = 200 turns/m (the number of turns per unit length)
Plugging in these values, we can calculate the current required:
I = 0.15 T / (4π × 10^⁻7 T m/A * 200 turns/m)
I ≈ 0.597 A
Therefore, the current that must flow through the wire to provide a magnetic field of 0.15 T at the center of the solenoid is approximately 0.597 A.
To determine if this current is reasonable, we need to compare it to the wire's safe carrying capacity.
Since the safe carrying capacity of the wire is not given in the question, we cannot make a direct comparison. However, in general, if the current required is significantly lower than the wire's safe carrying capacity, it can be considered reasonable.
Therefore, to determine if the current is reasonable, we need to compare it to the safe carrying capacity of the wire as specified by the manufacturer or relevant standards.
1) To determine if the technician can construct the desired solenoid, we need to calculate the number of turns required.
Given:
Maximum current (I) = 5 A
Magnetic field at center (B) = 0.06 T
Safe winding density = 10 loops/cm
To find the number of turns, we need to calculate the number of loops per meter.
Number of loops/meter = Safe winding density (loops/cm) * 100 (cm/m) = 10 loops/cm * 100 cm/m = 1000 loops/m
The magnetic field inside a solenoid is given by the formula:
B = (μ₀ * N * I) / L
Where:
B is the magnetic field
μ₀ is the permeability of free space
N is the number of turns
I is the current
L is the length of the solenoid
We can rearrange the formula to solve for N:
N = (B * L) / (μ₀ * I)
The permeability of free space (μ₀) is a constant equal to 4π * 10^(-7) T m/A.
Plugging in the values:
N = (0.06 T * L) / (4π * 10^(-7) T m/A * 5 A)
Assuming L is in meters, we can calculate the number of turns required.
2) Plugging in the values:
N = (0.06 T * 0.25 m) / (4π * 10^(-7) T m/A * 5 A)
N ≈ 9.5493
Since the number of turns required is approximately 9.5493, which cannot be achieved with whole numbers, the technician will not be able to construct the desired solenoid with this wire.
2) To calculate the current required to produce a magnetic field of 0.15 T at the center of the solenoid, we can use the same formula as before:
B = (μ₀ * N * I) / L
Rearranging the formula to solve for I:
I = (B * L) / (μ₀ * N)
Plugging in the values:
I = (0.15 T * 0.25 m) / (4π * 10^(-7) T m/A * N)
Assuming N is the number of turns, we can calculate the current required.
Additionally, the reasonableness of the calculated current depends on the specific application and context. Generally, it is recommended to consider safety guidelines and the wire's maximum current-carrying capacity to determine if the calculated current is reasonable.