Two long, straight wires are separated by 0.12 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates.

(a) Find the magnitude of the net magnetic field at the point A.
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(b) Find the magnitude of the net magnetic field at the point B.
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This math is correct except that u0 = [(4)(pi)]x10^-7, not positive 7. Otherwise, thanks for your work.

B=μ0I/2πr

B1 = (4π×10^7)(8.0A)/(2π×0.030m)
B2 = (4π×10^7)(-8.0A)/(2π×0.150m)
BA = B1 + B2

B1 = (4π×10^7)(8.0A)/(2π×0.060m)
B2 = (4π×10^7)(-8.0A)/(2π×-0.060m)
BB = B1 + B2

To find the magnitude of the net magnetic field at point A and B, you can use the Biot-Savart law, which states that the magnetic field produced by a straight current-carrying wire is directly proportional to the magnitude of the current and inversely proportional to the distance from the wire.

(a) To find the magnetic field at point A:

1. Use the right-hand rule to determine the direction of the magnetic fields produced by each wire. Since the currents are in opposite directions, the magnetic fields will be pointing in opposite directions as well.

2. Use the Biot-Savart law to find the magnetic field produced by each wire:
B1 = (μ0 * I1) / (2π * r)
B2 = (μ0 * I2) / (2π * r)
where μ0 is the permeability of free space (4π * 10^-7 T*m/A) and r is the distance from the wire.

3. Calculate the net magnetic field at point A:
B_net = B1 - B2

Given:
Current in wire 1 (I1) = 8.0 A
Current in wire 2 (I2) = -8.0 A (opposite direction)
Distance between the wires (r) = 0.12 m

Substituting the values into the equations, we get:
B1 = (4π * 10^-7 T*m/A * 8.0 A) / (2π * 0.12 m)
B2 = (4π * 10^-7 T*m/A * -8.0 A) / (2π * 0.12 m)

Simplifying, we find:
B1 = 3.33 * 10^-6 T
B2 = -3.33 * 10^-6 T

Therefore, the magnitude of the net magnetic field at point A is:
B_net = |B1 - B2|
= |3.33 * 10^-6 T - (-3.33 * 10^-6 T)|
= 6.66 * 10^-6 T or 6.7 μT (rounded to two decimal places).

(b) To find the magnetic field at point B:

The magnetic field produced by each wire at point B will have the same direction.

4. Calculate the net magnetic field at point B:
B_net = B1 + B2

Substituting the values into the equations, we get:
B1 = (4π * 10^-7 T*m/A * 8.0 A) / (2π * 0.12 m)
B2 = (4π * 10^-7 T*m/A * 8.0 A) / (2π * 0.12 m)

Simplifying, we find:
B1 = 3.33 * 10^-6 T
B2 = 3.33 * 10^-6 T

Therefore, the magnitude of the net magnetic field at point B is:
B_net = |B1 + B2|
= |3.33 * 10^-6 T + 3.33 * 10^-6 T|
= 6.66 * 10^-6 T or 6.7 μT (rounded to two decimal places).

To find the magnitude of the net magnetic field at points A and B, you can use the equation for the magnetic field produced by a long, straight wire:

B = (μ₀ * I) / (2π * r)

In this equation, B represents the magnitude of the magnetic field, μ₀ is the permeability of free space (equal to 4π × 10⁻⁷ T·m/A), I is the current in the wire, and r is the distance from the wire to the point where you want to find the magnetic field.

(a) To find the magnitude of the net magnetic field at point A, you need to consider the magnetic fields produced by both wires. The wire on the left has a current of 8.0 A, and the wire on the right has a current of -8.0 A (since the currents are in opposite directions). The distance between the wires and point A is given as 0.12 m.

Let's calculate the magnetic field produced by each wire:

B₁ = (μ₀ * I₁) / (2π * r) = (4π × 10⁻⁷ T·m/A * 8.0 A) / (2π * 0.12 m)
= (32π × 10⁻⁷ T·m) / (2π * 0.12 m)
= (32π × 10⁻⁷ T·m) / (0.24π m)
= 133.3 × 10⁻⁷ T

B₂ = (μ₀ * I₂) / (2π * r) = (4π × 10⁻⁷ T·m/A * -8.0 A) / (2π * 0.12 m)
= (-32π × 10⁻⁷ T·m) / (0.24π m)
= -133.3 × 10⁻⁷ T

The net magnetic field at point A is the sum of the magnetic fields produced by both wires:

B_net_A = B₁ + B₂ = 133.3 × 10⁻⁷ T + (-133.3 × 10⁻⁷ T)
= 0 T

Therefore, the magnitude of the net magnetic field at point A is zero Tesla.

(b) To find the magnitude of the net magnetic field at point B, you can use the same approach. The distance between the wires and point B is also 0.12 m.

Again, let's calculate the magnetic field produced by each wire:

B₃ = (μ₀ * I₃) / (2π * r) = (4π × 10⁻⁷ T·m/A * 8.0 A) / (2π * 0.12 m)
= (32π × 10⁻⁷ T·m) / (0.24π m)
= 133.3 × 10⁻⁷ T

B₄ = (μ₀ * I₄) / (2π * r) = (4π × 10⁻⁷ T·m/A * -8.0 A) / (2π * 0.12 m)
= (-32π × 10⁻⁷ T·m) / (0.24π m)
= -133.3 × 10⁻⁷ T

The net magnetic field at point B is the sum of the magnetic fields produced by both wires:

B_net_B = B₃ + B₄ = 133.3 × 10⁻⁷ T + (-133.3 × 10⁻⁷ T)
= 0 T

Therefore, the magnitude of the net magnetic field at point B is zero Tesla.