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Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above?
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Consider the following system. Two circular loopsof wire are placed ho...
Introduction:
In this system, two circular loops of wire are placed horizontally, with a common axis passing vertically through the center of each coil. The lower loop has a radius 'r' and carries a current 'i', while the upper loop has a much larger radius 'R' and is positioned at a distance 'x' above the lower loop. This system creates a magnetic field that can be analyzed using the principles of electromagnetism.
Magnetic Field of a Current-Carrying Loop:
A current-carrying loop produces a magnetic field that can be calculated using Ampere's law. The magnetic field at a point on the axis of a circular loop is given by the equation:
B = (μ₀ * i * r²) / (2 * (r² + x²)^(3/2))
where B is the magnitude of the magnetic field, μ₀ is the permeability of free space, i is the current flowing through the loop, r is the radius of the loop, and x is the distance between the center of the loop and the point on the axis where the magnetic field is being calculated.
Effect of Distance on Magnetic Field:
As the distance 'x' from the center of the lower loop increases, the magnitude of the magnetic field decreases. This is because the magnetic field follows an inverse square law, where the field strength is inversely proportional to the square of the distance from the source. In this case, the magnetic field at a point on the axis of the lower loop decreases as the distance 'x' increases.
Effect of Radius on Magnetic Field:
The radius 'r' of the lower loop also affects the magnetic field. As the radius increases, the magnetic field becomes stronger. However, the effect of the radius is overshadowed by the effect of distance in this system, as the upper loop has a much larger radius 'R' and is positioned at a distance 'x' above the lower loop. Therefore, the magnetic field due to the upper loop dominates the magnetic field due to the lower loop.
Conclusion:
In conclusion, the system of two circular loops of wire produces a magnetic field that can be analyzed using the principles of electromagnetism. The magnetic field at a point on the axis of the lower loop can be calculated using Ampere's law, taking into account the current, radius, and distance from the center of the lower loop. The magnetic field decreases as the distance from the center of the lower loop increases, following an inverse square law. The radius of the lower loop also affects the magnetic field, but its effect is overshadowed by the much larger radius of the upper loop.
In this system, two circular loops of wire are placed horizontally, with a common axis passing vertically through the center of each coil. The lower loop has a radius 'r' and carries a current 'i', while the upper loop has a much larger radius 'R' and is positioned at a distance 'x' above the lower loop. This system creates a magnetic field that can be analyzed using the principles of electromagnetism.
Magnetic Field of a Current-Carrying Loop:
A current-carrying loop produces a magnetic field that can be calculated using Ampere's law. The magnetic field at a point on the axis of a circular loop is given by the equation:
B = (μ₀ * i * r²) / (2 * (r² + x²)^(3/2))
where B is the magnitude of the magnetic field, μ₀ is the permeability of free space, i is the current flowing through the loop, r is the radius of the loop, and x is the distance between the center of the loop and the point on the axis where the magnetic field is being calculated.
Effect of Distance on Magnetic Field:
As the distance 'x' from the center of the lower loop increases, the magnitude of the magnetic field decreases. This is because the magnetic field follows an inverse square law, where the field strength is inversely proportional to the square of the distance from the source. In this case, the magnetic field at a point on the axis of the lower loop decreases as the distance 'x' increases.
Effect of Radius on Magnetic Field:
The radius 'r' of the lower loop also affects the magnetic field. As the radius increases, the magnetic field becomes stronger. However, the effect of the radius is overshadowed by the effect of distance in this system, as the upper loop has a much larger radius 'R' and is positioned at a distance 'x' above the lower loop. Therefore, the magnetic field due to the upper loop dominates the magnetic field due to the lower loop.
Conclusion:
In conclusion, the system of two circular loops of wire produces a magnetic field that can be analyzed using the principles of electromagnetism. The magnetic field at a point on the axis of the lower loop can be calculated using Ampere's law, taking into account the current, radius, and distance from the center of the lower loop. The magnetic field decreases as the distance from the center of the lower loop increases, following an inverse square law. The radius of the lower loop also affects the magnetic field, but its effect is overshadowed by the much larger radius of the upper loop.
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Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above?
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Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above?.
Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above?.
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Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above?, a detailed solution for Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? has been provided alongside types of Consider the following system. Two circular loopsof wire are placed horizontally, having a commonaxis passing vertically through the centre of each coil (see figure). The lower loop has radius ‘r’ andcarries a current ‘i’ as shown in the figure. Theupper loop has a radius R (R >> r) and is at adistance x (x >> R) above? theory, EduRev gives you an
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