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Three uniform current sheets are located in free space as follows: 8uz A/m at y = 0, -4uz A/m at y = 1 and -4uz A/m at y = -1. Let F be the vector force per meter length exerted on a current filament carrying 7 mA in the uL direction.
Que: If the current filament is located at y = 0.5, z = 0, and uL = ux, then F is
  • a)
    35.2 uy nN/m
  • b)
    68.3  ux nN/m
  • c)
    105.6 uz nN/m
  • d)
    0
Correct answer is option 'D'. Can you explain this answer?
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Three uniform current sheets are located in free space as follows: 8uz...
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Three uniform current sheets are located in free space as follows: 8uz...
Given:
- Three uniform current sheets located in free space.
- Current density of the sheets:
- 8 u_z A/m at y = 0,
- -4 u_z A/m at y = 1, and
- -4 u_z A/m at y = -1.
- Current filament carrying 7 mA in the u_L direction located at y = 0.5, z = 0, and u_L = u_x.

To find: The vector force per meter length (F) exerted on the current filament.

Approach:
1. Calculate the magnetic field created by each current sheet at the position of the filament.
2. Calculate the total magnetic field at the position of the filament by summing the contributions from each current sheet.
3. Calculate the force on the current filament using the formula F = I * L x B, where I is the current, L is the length vector of the filament, and B is the magnetic field.
4. Determine the direction and magnitude of the force.

Calculation:
1. Magnetic field created by each current sheet:
- Magnetic field due to the current sheet at y = 0:
- At the position of the filament (y = 0.5, z = 0), the distance from the current sheet is 0.5 m.
- Using the formula for the magnetic field due to a current sheet, B = μ_0 * J * h, where μ_0 is the permeability of free space, J is the current density, and h is the distance from the current sheet:
- B = μ_0 * 8 u_z A/m * 0.5 m = 4π * 10^(-7) * 8 u_z T
- Magnetic field due to the current sheet at y = 1:
- At the position of the filament (y = 0.5, z = 0), the distance from the current sheet is 0.5 m in the negative y-direction.
- Using the same formula as above, B = μ_0 * (-4 u_z A/m) * 0.5 m = -2π * 10^(-7) * 4 u_z T
- Magnetic field due to the current sheet at y = -1:
- At the position of the filament (y = 0.5, z = 0), the distance from the current sheet is 1.5 m in the positive y-direction.
- Using the same formula as above, B = μ_0 * (-4 u_z A/m) * 1.5 m = -6π * 10^(-7) * 4 u_z T

2. Total magnetic field at the position of the filament:
- Summing the contributions from each current sheet, B_total = 4π * 10^(-7) * 8 u_z T - 2π * 10^(-7) * 4 u_z T - 6π * 10^(-7) * 4 u_z T = -2π * 10^(-7) * 8 u_z T

3. Force on the current filament:
- Length vector of the filament, L = u_L = u_x
- Current, I = 7 mA = 7 * 10^(-
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Three uniform current sheets are located in free space as follows: 8uzA/m at y = 0, -4uzA/m at y = 1 and -4uzA/m at y = -1. Let F be the vector force per meter length exerted on a current filament carrying 7 mA in the uLdirection.Que: If the current filament is located at y = 0.5, z = 0, anduL= ux, then F isa)35.2 uynN/mb)68.3 ux nN/mc)105.6 uz nN/md)0Correct answer is option 'D'. Can you explain this answer?
Question Description
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