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Two infinitely long parallel filaments each carry 100 A in the uz direction. If the filaments lie in the plane y = 0 at x = 0 and x = 5 mm, the force on the filament passing through the origin is
- a)0.4 ux N/m
- b)-0.4 ux N/m
- c)4ux mN/m
- d)-4ux mN/m
Correct answer is option 'A'. Can you explain this answer?
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Two infinitely long parallel filaments each carry 100 A in the uzdirec...
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Understanding the Problem
In this scenario, we have two infinitely long parallel filaments carrying a current of 100 A in the positive z-direction. One filament is located at the origin (x=0, y=0) and the other at (x=5 mm, y=0).
Magnetic Field Due to a Current-Carrying Wire
- The magnetic field (B) generated by a long straight current-carrying filament is given by the formula:
B = (μ₀ * I) / (2 * π * r)
where μ₀ is the permeability of free space, I is the current, and r is the distance from the wire.
- For the filament at the origin, the magnetic field at the location of the second filament (x=5 mm) can be calculated using r = 5 mm = 0.005 m.
Calculating the Magnetic Field
- Substituting the values:
B = (4π × 10^-7 T*m/A * 100 A) / (2 * π * 0.005 m)
This simplifies to B = 4 × 10^-2 T (directed into the plane of the page).
Force on the Second Filament
- The force (F) experienced by a current-carrying wire in a magnetic field is given by:
F = I * L × B
Here, L is the length vector of the wire.
- The second filament also carries a current of 100 A in the uz direction, so the force on it due to the magnetic field from the first filament is calculated.
Direction of the Force
- Using the right-hand rule, the force on the filament at (5 mm, 0) will be directed along the negative x-direction (to the left), resulting in:
F = -4 × 10^-1 ux N/m.
Conclusion
Thus, the correct answer is: 0.4 ux N/m (option 'a'). The negative sign indicates the force direction, confirming the force acting on the filament at the origin due to the other filament.
In this scenario, we have two infinitely long parallel filaments carrying a current of 100 A in the positive z-direction. One filament is located at the origin (x=0, y=0) and the other at (x=5 mm, y=0).
Magnetic Field Due to a Current-Carrying Wire
- The magnetic field (B) generated by a long straight current-carrying filament is given by the formula:
B = (μ₀ * I) / (2 * π * r)
where μ₀ is the permeability of free space, I is the current, and r is the distance from the wire.
- For the filament at the origin, the magnetic field at the location of the second filament (x=5 mm) can be calculated using r = 5 mm = 0.005 m.
Calculating the Magnetic Field
- Substituting the values:
B = (4π × 10^-7 T*m/A * 100 A) / (2 * π * 0.005 m)
This simplifies to B = 4 × 10^-2 T (directed into the plane of the page).
Force on the Second Filament
- The force (F) experienced by a current-carrying wire in a magnetic field is given by:
F = I * L × B
Here, L is the length vector of the wire.
- The second filament also carries a current of 100 A in the uz direction, so the force on it due to the magnetic field from the first filament is calculated.
Direction of the Force
- Using the right-hand rule, the force on the filament at (5 mm, 0) will be directed along the negative x-direction (to the left), resulting in:
F = -4 × 10^-1 ux N/m.
Conclusion
Thus, the correct answer is: 0.4 ux N/m (option 'a'). The negative sign indicates the force direction, confirming the force acting on the filament at the origin due to the other filament.
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Two infinitely long parallel filaments each carry 100 A in the uzdirection. If the filaments lie in the plane y = 0 at x =0 and x =5 mm, the force on the filament passing through the origin isa)0.4 ux N/mb)-0.4ux N/mc)4uxmN/md)-4ux mN/mCorrect answer is option 'A'. Can you explain this answer?
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