A current I=2.3 A flows around a continuous path that consists of portions of two concentric circles of radii a and a/2, respectively, where a=5 cm, and two straight radial segments. The point P is at the common center of the two circle segments.

Calculate the components of the magnetic field (in T) at point P.
Bx=

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By=

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Bz=

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To calculate the components of the magnetic field at point P, we can use the Biot-Savart Law. This law states that the magnetic field at a point due to a current-carrying wire segment is directly proportional to the current, the length of the segment, and the angle between the two.

Considering the geometry described in the problem, let's break down the magnetic field into its x, y, and z-components:

1. Bx (the component in the x-direction):
- The magnetic field due to the circular segments will have no x-component because they lie in the y-z plane.
- Only the radial segments contribute to the x-component.
- The magnitude of the magnetic field at point P due to a straight wire segment is given by the equation B = (μ₀ * I) / (2π * r), where μ₀ is the permeability of free space, I is the current, and r is the distance between the wire and the point where we want to calculate the magnetic field.
- In this case, we have two radial segments, one going towards P and the other away from P.
- The contribution of the segment going towards P is B1x = (μ₀ * I) / (2π * (a + a/2)).
- The contribution of the segment going away from P is B2x = -(μ₀ * I) / (2π * (a - a/2)).
- The total x-component of the magnetic field at point P is Bx = B1x + B2x.

2. By (the component in the y-direction):
- The magnetic field due to the circular segments will have a y-component because they lie in the y-z plane.
- The magnitude of the magnetic field at point P due to a circular wire segment is given by the equation B = (μ₀ * I * θ) / (2 * π * r), where θ is the angle subtended by the circular segment.
- For the larger circular segment, the angle θ1 can be found using the formula θ = 2π * (a / (2 * π * a)) = π.
- For the smaller circular segment, the angle θ2 can be found using the formula θ = 2π * (a / (2 * π * (a/2))) = 2π.
- The contribution of the larger circular segment is By1 = (μ₀ * I * π) / (2 * π * a).
- The contribution of the smaller circular segment is By2 = (μ₀ * I * 2π) / (2 * π * (a/2)).
- The total y-component of the magnetic field at point P is By = By1 + By2.

3. Bz (the component in the z-direction):
- The magnetic field due to the circular segments will have a z-component because they lie in the y-z plane.
- The magnitude of the magnetic field at point P due to a circular wire segment is zero at the center of the circular segment.
- This means that the z-component of the magnetic field due to the circular segments is zero at point P.
- The radial segments also do not contribute to the z-component.
- Therefore, the z-component of the magnetic field at point P is Bz = 0.

Now, you can substitute the values of the given variables (such as a = 5 cm and I = 2.3 A) into the equations to calculate the components of the magnetic field at point P.