GATE Exam > GATE Questions > An infinitely long straight wire is carrying ...
Start Learning for Free
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.
Correct answer is '4 to 4'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
An infinitely long straight wire is carrying a steady current I. The r...
**Explanation:**
To find the ratio of magnetic energy density at distance r1 to that at distance r2 from the wire, we need to consider the magnetic field produced by the current-carrying wire at these distances.
**1. Magnetic Field at Distance r1:**
The magnetic field produced by an infinitely long straight wire at a distance r from the wire is given by Ampere's Law:
B = (μ₀I)/(2πr)
where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the wire.
**2. Magnetic Energy Density at Distance r1:**
The magnetic energy density (u) at a point is given by the equation:
u = (B²)/(2μ₀)
Substituting the expression for B, we get:
u₁ = [(μ₀I)/(2πr₁)]² / (2μ₀)
= (μ₀I)² / (4π²r₁² * 2μ₀)
= (μ₀I)² / (8π²r₁²)
**3. Magnetic Field at Distance r2(= 2r1):**
The magnetic field at distance r2 is:
B₂ = (μ₀I)/(2πr₂)
= (μ₀I)/(2π(2r₁))
= (μ₀I)/(4πr₁)
**4. Magnetic Energy Density at Distance r2:**
The magnetic energy density at distance r2 is:
u₂ = [(μ₀I)/(4πr₁)]² / (2μ₀)
= (μ₀I)² / (16π²r₁² * 2μ₀)
= (μ₀I)² / (32π²r₁²)
**5. Ratio of Magnetic Energy Density:**
To find the ratio of magnetic energy density at r1 to that at r2, we divide u₁ by u₂:
(u₁/u₂) = [(μ₀I)² / (8π²r₁²)] / [(μ₀I)² / (32π²r₁²)]
= (μ₀I)² / (8π²r₁²) * (32π²r₁² / (μ₀I)²)
= 4
Therefore, the ratio of magnetic energy density at distance r1 to that at distance r2 is 4 to 4.
To find the ratio of magnetic energy density at distance r1 to that at distance r2 from the wire, we need to consider the magnetic field produced by the current-carrying wire at these distances.
**1. Magnetic Field at Distance r1:**
The magnetic field produced by an infinitely long straight wire at a distance r from the wire is given by Ampere's Law:
B = (μ₀I)/(2πr)
where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the wire.
**2. Magnetic Energy Density at Distance r1:**
The magnetic energy density (u) at a point is given by the equation:
u = (B²)/(2μ₀)
Substituting the expression for B, we get:
u₁ = [(μ₀I)/(2πr₁)]² / (2μ₀)
= (μ₀I)² / (4π²r₁² * 2μ₀)
= (μ₀I)² / (8π²r₁²)
**3. Magnetic Field at Distance r2(= 2r1):**
The magnetic field at distance r2 is:
B₂ = (μ₀I)/(2πr₂)
= (μ₀I)/(2π(2r₁))
= (μ₀I)/(4πr₁)
**4. Magnetic Energy Density at Distance r2:**
The magnetic energy density at distance r2 is:
u₂ = [(μ₀I)/(4πr₁)]² / (2μ₀)
= (μ₀I)² / (16π²r₁² * 2μ₀)
= (μ₀I)² / (32π²r₁²)
**5. Ratio of Magnetic Energy Density:**
To find the ratio of magnetic energy density at r1 to that at r2, we divide u₁ by u₂:
(u₁/u₂) = [(μ₀I)² / (8π²r₁²)] / [(μ₀I)² / (32π²r₁²)]
= (μ₀I)² / (8π²r₁²) * (32π²r₁² / (μ₀I)²)
= 4
Therefore, the ratio of magnetic energy density at distance r1 to that at distance r2 is 4 to 4.
Free Test
FREE
| Start Free Test |
Community Answer
An infinitely long straight wire is carrying a steady current I. The r...
Explain the answer plz
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer?
Question Description
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer?.
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer?.
Solutions for An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer?, a detailed solution for An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? has been provided alongside types of An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance r1 to that at r2(= 2 r1) from the wire is ________.Correct answer is '4 to 4'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup