The figure shows a cross section of three parallel wires each carrying a current of 15 A. The currents in wires A and B are into paper, while that in wire C is out of the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire C?
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Ah, the magical world of physics! Let me entertain you with my electrifying humor while answering your question.
So, we have wire A and wire B walking into a bar, and wire C decides to walk out. They all carry a current of 15 A, ready for some magnetic force action.
Now, imagine wire C as a superhero cape, stretching over a distance of 4.0m. And what happens when you wear a cape? Well, you feel a tremendous force of attraction. In this case, the force is generated by the magnetic field created by wires A and B.
Using the right-hand rule, we can calculate the magnitude of the force on wire C by multiplying the current (15 A) by the distance between the wires (R = 5.0 mm).
But before we do that, let me remind you that wire C is just passing through the party, so the force is going to be a little hostile. Let's call it F, the Incredible Force of C.
Alright, F = I * B * L, where I is the current, B is the magnetic field, and L is the length of wire C.
Since wire C is perpendicular to the plane, we can simplify the formula to F = I * B * L.
Now, we know the current (15 A), the length (4.0 m), and the distance (R = 5.0 mm). Plug these values into the formula, and voila! You'll have your answer in no time.
Just remember, my friend, whenever you meet wires A, B, and C, make sure you're ready for a shocking encounter. Electricity and magnetism sure know how to put on a show!
Good luck with your calculations, and may the magnetic force be with wire C!
To find the magnitude of the force on wire C, we can use the right-hand rule for magnetic fields.
Step 1: Determine the magnetic field created by wires A and B at the location of wire C.
The magnetic field created by a long straight wire can be found using the formula: B = (μ₀ * I) / (2π * r), where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current in the wire, and r is the distance from the wire.
For wire A:
B₁ = (4π × 10⁻⁷ * 15) / (2π * 0.005)
B₁ = (2 * 10⁻⁶) T
For wire B:
B₂ = (4π × 10⁻⁷ * 15) / (2π * 0.005)
B₂ = (2 * 10⁻⁶) T
Since the currents in wires A and B are in the same direction, the magnetic fields add up to:
B_total = B₁ + B₂
B_total = (4 * 10⁻⁶) T
Step 2: Calculate the force on wire C using the formula: F = B * I * L, where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.
F = (4 * 10⁻⁶) * 15 * 4
F = 0.24 N
Therefore, the magnitude of the force on a 4.0-m length of wire C is 0.24 N.
To calculate the magnitude of the force on a length of wire C, we can use the right-hand rule for magnetic fields.
1. Determine the direction of the magnetic field produced by wires A and B at the location of wire C.
- Since the currents in wires A and B are both into the paper, the magnetic field around each wire will form clockwise circles when viewed from above the paper.
2. Use the right-hand rule to determine the direction of the magnetic field due to wire C at the location of wire C.
- To use the right-hand rule, point the thumb of your right hand in the direction of the current in wire C (out of the paper). Your curled fingers will show the direction of the magnetic field around wire C. In this case, the magnetic field will form counterclockwise circles when viewed from above the paper.
3. Calculate the magnitude of the force using the formula:
F = |I1| * |I2| * L * B * sin(θ)
- I1 is the current in wire 1 (wire C in this case) = 15 A
- I2 is the current in wire 2 (wire A or B) = 15 A
- L is the length of wire 1 (wire C) = 4 m
- B is the magnitude of the magnetic field
- θ is the angle between the current and magnetic field vectors (in this case, 90 degrees, since the wires are perpendicular)
4. Calculate the magnitude of the magnetic field at the location of wire C:
B = μ₀ * I2 / 2πR
- μ₀ is the permeability of free space (4π x 10⁻⁷ T ⋅ m/A)
- I2 is the current in wire 2 (15 A)
- R is the distance between the wires (5.0 mm = 0.005 m)
5. Substitute the values into the formula:
F = 15 A * 15 A * 4 m * (4π x 10⁻⁷ T ⋅ m/A) / (0.005 m) * sin(90°)
6. Simplify the formula and calculate the magnitude of the force.
Following these steps, you can solve for the magnitude of the force on the 4.0-m length of wire C.