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Two straight parallel wires carry currents of I = 12.5 A and I = 11.6 A in opposite directions as shown in the figure. Point A is the midpoint between the wires. The total distance between the wires is d = 10.0 cm.

a) Calculate the value of the magnetic field created by I at point A.
b) Calculate the value of the magnetic field created by I2 at point A.
c) What is the net magnetic field at point A?
d) What is the direction of the net magnetic field?

User Six Quads
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Final answer:

a) The magnetic field created by I at point A is 5.0 × 10^-5 T. b) The magnetic field created by I₂ at point A is 4.6 × 10^-5 T. c) The net magnetic field at point A is 9.6 × 10^-5 T. d) The direction of the net magnetic field is opposite to the magnetic field created by I.

Step-by-step explanation:

a) To calculate the magnetic field created by I at point A, we can use the formula for the magnetic field created by a straight wire:

B = (μ₀ * I) / (2 * π * r)

where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), I is the current, and r is the distance from the wire. Since point A is the midpoint between the wires, the distance from each wire to point A is d/2 = 5.0 cm. Plugging in the values, we get:

B₁ = (4π × 10^-7 T·m/A * 12.5 A) / (2 * π * 0.05 m) = 5.0 × 10^-5 T

b) To calculate the magnetic field created by I₂ at point A, we can use the same formula:

B₂ = (μ₀ * I₂) / (2 * π * r)

Using the same distance of 5.0 cm, we get:

B₂ = (4π × 10^-7 T·m/A * 11.6 A) / (2 * π * 0.05 m) = 4.6 × 10^-5 T

c) The net magnetic field at point A is the vector sum of the magnetic fields created by I and I₂:

B_net = B₁ + B₂ = 5.0 × 10^-5 T + 4.6 × 10^-5 T = 9.6 × 10^-5 T

d) The direction of the net magnetic field depends on the direction of the individual magnetic fields created by I and I₂. Since the currents in the wires are in opposite directions, the magnetic fields created by each wire have opposite directions. Therefore, the net magnetic field at point A would have a direction opposite to the magnetic field created by I.

User Trick Kramer
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