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A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is?
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A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is u...
Introduction
To find the ratio of the magnetic field B at a distance a/2 from the center of a long straight wire carrying current i, and the magnetic field B' at a distance 2a, we can use Ampère's Law.
Magnetic Field Inside the Wire (r < />
- For a long straight wire with radius a, the magnetic field inside (at r = a/2) is given by:
- B = (μ₀ * i * r) / (2 * π * a²)
- Here, μ₀ is the permeability of free space and the current is uniformly distributed.
Magnetic Field Outside the Wire (r > a)
- For points outside the wire (at r = 2a), the magnetic field is calculated as:
- B' = (μ₀ * i) / (2 * π * r)
- Therefore, B' = (μ₀ * i) / (4 * π * a)
Calculating the Ratio B/B'
- Now, we can set up the ratio of B to B':
- B = (μ₀ * i * (a/2)) / (2 * π * a²) = (μ₀ * i) / (4 * π * a)
- B' = (μ₀ * i) / (4 * π * a)
- Thus, we calculate the ratio:
- B/B' = [(μ₀ * i) / (4 * π * a)] / [(μ₀ * i) / (4 * π * a)] = 1
Conclusion
- The ratio of the magnetic field B at a distance a/2 from the axis of the wire to the magnetic field B' at a distance 2a is:
- B/B' = 1
This means that the magnetic fields at these two distances are equal, showcasing the effects of current distribution and radial distance in a long straight wire.
To find the ratio of the magnetic field B at a distance a/2 from the center of a long straight wire carrying current i, and the magnetic field B' at a distance 2a, we can use Ampère's Law.
Magnetic Field Inside the Wire (r < />
- For a long straight wire with radius a, the magnetic field inside (at r = a/2) is given by:
- B = (μ₀ * i * r) / (2 * π * a²)
- Here, μ₀ is the permeability of free space and the current is uniformly distributed.
Magnetic Field Outside the Wire (r > a)
- For points outside the wire (at r = 2a), the magnetic field is calculated as:
- B' = (μ₀ * i) / (2 * π * r)
- Therefore, B' = (μ₀ * i) / (4 * π * a)
Calculating the Ratio B/B'
- Now, we can set up the ratio of B to B':
- B = (μ₀ * i * (a/2)) / (2 * π * a²) = (μ₀ * i) / (4 * π * a)
- B' = (μ₀ * i) / (4 * π * a)
- Thus, we calculate the ratio:
- B/B' = [(μ₀ * i) / (4 * π * a)] / [(μ₀ * i) / (4 * π * a)] = 1
Conclusion
- The ratio of the magnetic field B at a distance a/2 from the axis of the wire to the magnetic field B' at a distance 2a is:
- B/B' = 1
This means that the magnetic fields at these two distances are equal, showcasing the effects of current distribution and radial distance in a long straight wire.
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A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is?
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A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is?.
A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A LONG STRAIGHT WIRE OF radius a carrues a current i. the current is uniformly distributed over its cross section. the ratio of the magnetic field B and B' At radial distances a/2 and 2a respectively , from the axis of wire is?.
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