#6 (6 points possible)
The demonstration in LS6.U5 uses a Helmholtz coil, which is a pair of wire coils along a common axis that creates a somewhat uniform magnetic field at the center. To achieve a uniform field, the coil separation is equal to the coil radius. The Helmholtz coil in the demo had a radius and separation of 37cm, and each coil has 400 turns of wire. If we sent 1.5A of current through the wires in the coil, in directions that makes their magnetic fields add (not cancel) in the region between them, what is the magnitude of the magnetic field in T at the center?
- unanswered
The demonstration in LS6.U5 uses a Helmholtz coil, which is a pair of wire coils along a common axis that creates a somewhat uniform magnetic field at the center. To achieve a uniform field, the coil separation is equal to the coil radius. The Helmholtz coil in the demo had a radius and separation of 37cm, and each coil has 400 turns of wire. If we sent 1.5A of current through the wires in the coil, in directions that makes their magnetic fields add (not cancel) in the region between them, what is the magnitude of the magnetic field in T at the
To find the magnitude of the magnetic field at the center of the Helmholtz coil, we can use the formula for the magnetic field produced by a current-carrying wire:
B = (μ0 * I * N) / (2 * R)
where B is the magnetic field, μ0 is the permeability of free space (4π * 10^(-7) T·m/A), I is the current, N is the number of turns, and R is the radius of the coil.
In this case, the radius of the coil is 37 cm or 0.37 m, the current is 1.5 A, and there are 400 turns in each coil.
Substituting these values into the formula, we get:
B = (4π * 10^(-7) T·m/A * 1.5 A * 400 turns) / (2 * 0.37 m)
Simplifying the expression, we get:
B = (1.884 * 10^(-4) T * turns) / (0.74 m)
B ≈ 0.255 T
Therefore, the magnitude of the magnetic field at the center of the Helmholtz coil is approximately 0.255 T.
To find the magnitude of the magnetic field at the center of the Helmholtz coil, we can use the formula for the magnetic field produced by a single circular loop of wire:
B = (μ0 * I * N) / (2 * R)
Where:
B = magnetic field (in Tesla)
μ0 = permeability of free space (approximately 4π × 10^-7 T m/A)
I = current (in Amperes)
N = number of turns of wire in the coil
R = radius of the coil
Since we have two coils and their magnetic fields add up, the total magnetic field at the center can be found by doubling the value of B.
Given:
Radius of each coil (R) = 37 cm = 0.37 m
Separation between the coils = radius of each coil (37 cm = 0.37 m)
Number of turns of wire (N) = 400
Current (I) = 1.5 A
Plugging the values into the formula:
B = (4π × 10^-7 T m/A) * (1.5 A) * (400) / (2 * 0.37 m)
simplifying gives:
B = (1.88496 × 10^-6 T) * (400 / 0.37)
B = 2.03514 × 10^-3 T
Since we doubled the magnetic field value to account for the two coils, the final magnitude of the magnetic field at the center of the Helmholtz coil is:
2 * 2.03514 × 10^-3 T = 4.07028 × 10^-3 T