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A rectangular loop of wire in free space joins points A(1, 0, 1) to B(3, 0, 1) to C(3, 0, 4) to D(1, 0, 4) to A. The wire carries a current of 6 mA flowing in the uz direction from B to C. A filamentary current of 15 A flows along the entire z, axis in the uz directions.
Que: The total force on the loop is
- a)36ux nN
- b)-36ux nN
- c)54ux nN
- d)-54ux nN
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A rectangular loop of wire in free space joins points A(1, 0, 1) to B(...
This will be the vector sum of the forces on the four sides. By symmetry, the forces on sides AB and CD will be equal and opposite, and so will cancel. This leaves the sum of forces on side BC and DA
Most Upvoted Answer
A rectangular loop of wire in free space joins points A(1, 0, 1) to B(...
Given Information:
- Rectangular loop of wire joining points A, B, C, D in free space
- Current of 6 mA flowing from B to C
- Filamentary current of 15 A along z-axis in uz direction
Calculating the Force:
1. Calculate the magnetic field due to the filamentary current along the z-axis at each corner of the loop (A, B, C, D).
2. Using the right-hand rule, determine the direction of the force acting on each segment of the loop due to the magnetic field.
3. Calculate the force on each segment of the loop and then sum up the forces to find the total force on the loop.
Determining the Total Force:
- The force due to the current along the z-axis on segments AB and CD would be in opposite directions, canceling each other out.
- The force on segments BC and DA would add up to give the total force on the loop.
- The total force would be in the direction perpendicular to the loop and can be calculated using the formula F = I * L * B * sin(θ), where I is the current, L is the length of the segment, B is the magnetic field, and θ is the angle between the current and the magnetic field.
Therefore, the total force on the loop is 36 uχ nN in the positive uχ direction.
- Rectangular loop of wire joining points A, B, C, D in free space
- Current of 6 mA flowing from B to C
- Filamentary current of 15 A along z-axis in uz direction
Calculating the Force:
1. Calculate the magnetic field due to the filamentary current along the z-axis at each corner of the loop (A, B, C, D).
2. Using the right-hand rule, determine the direction of the force acting on each segment of the loop due to the magnetic field.
3. Calculate the force on each segment of the loop and then sum up the forces to find the total force on the loop.
Determining the Total Force:
- The force due to the current along the z-axis on segments AB and CD would be in opposite directions, canceling each other out.
- The force on segments BC and DA would add up to give the total force on the loop.
- The total force would be in the direction perpendicular to the loop and can be calculated using the formula F = I * L * B * sin(θ), where I is the current, L is the length of the segment, B is the magnetic field, and θ is the angle between the current and the magnetic field.
Therefore, the total force on the loop is 36 uχ nN in the positive uχ direction.
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A rectangular loop of wire in free space joins points A(1, 0, 1) to B(3, 0, 1) to C(3, 0, 4) to D(1, 0, 4) to A. The wire carries a current of 6 mA flowing in the uzdirection from B to C. A filamentary current of 15 A flows along the entire z, axis in the uzdirections.Que: The total force on the loop isa)36ux nNb)-36ux nNc)54ux nNd)-54ux nNCorrect answer is option 'A'. Can you explain this answer?
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