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Two parallel conducting rings, both of radius R, are separated by a distance R. The planes of the rings are perpendicular to the line joining their centres, which is taken to be the x-axis.

If both the rings carry the same current i along the same direction, the magnitude of the magnetic field along the x- axis is best represented by
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two parallel conducting rings, both of radius R, are separated by a di...
Concept:
The magnetic field B produced by a ring at any point on the axial line is defined by Ampere's circuital law as: where:
  • μ0 is the permeability of free space,
  • i is the current flowing through the wire,
  • r is the radius of the circular wire,
  • z is the position of a point on the axis from the center of the coil.
Explanation:
Since there are two rings here, and they both have the same current in the same direction, they will each produce a magnetic field that combines at points along the x-axis.
Notice that the magnetic field produced by each ring along the x-axis is symmetrical with respect to the x-axis, and they will combine constructively.
The total magnetic field would be twice the magnetic field produced by one of the rings because of the constructive superposition.
When the distance between rings is R,which leads to a uniform magnetic field at the center region. At this condition, magnetic fields at the planes of the coil are a little bit smaller than that at the center. So, Option 1 is an approximate diagram.
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Two parallel conducting rings, both of radius R, are separated by a distance R. The planes of the rings are perpendicular to the line joining their centres, which is taken to be the x-axis.If both the rings carry the same current i along the same direction, the magnitude of the magnetic field along the x- axis is best represented bya)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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