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A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.?
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A solenoid has turn density 5000 turn/m and cross sectional area 10 cm...
Given:
- Turn density of solenoid = 5000 turns/m
- Cross-sectional area of solenoid = 10 cm^2 = 0.001 m^2
- Current flowing in the solenoid = 1 A
- Relative permeability of the inside material = 1000
To find: Energy per unit length of solenoid
Solution:
Step 1: Calculate the magnetic field inside the solenoid
- Magnetic field inside the solenoid is given by B = μ₀nI, where μ₀ is the permeability of free space, n is the turn density and I is the current
- μ₀ = 4π × 10^-7 Tm/A
- n = 5000 turns/m
- I = 1 A
- B = μ₀nI = 4π × 10^-7 Tm/A × 5000 turns/m × 1 A = 0.002 T
Step 2: Calculate the magnetic flux density inside the solenoid
- Magnetic flux density, B = μH, where H is the magnetic field intensity and μ is the relative permeability
- H = B/μ = 0.002 T/1000 = 2 × 10^-6 T
- Therefore, magnetic flux density inside the solenoid is 2 × 10^-6 T
Step 3: Calculate the energy per unit volume of the magnetic field inside the solenoid
- Energy per unit volume of the magnetic field, u = 1/2μB^2
- u = 1/2 × 4π × 10^-7 Tm/A × (0.002 T)^2 = 1.256 × 10^-9 J/m^3
Step 4: Calculate the energy per unit length of the solenoid
- Energy per unit length of the solenoid, U = uAL
- A = 0.001 m^2 (given)
- L = 1 m (as we are calculating energy per unit length)
- Therefore, U = 1.256 × 10^-9 J/m^3 × 0.001 m^2 × 1 m = 1.256 × 10^-12 J/m
Answer: The energy per unit length of the solenoid is 1.256 × 10^-12 J/m.
- Turn density of solenoid = 5000 turns/m
- Cross-sectional area of solenoid = 10 cm^2 = 0.001 m^2
- Current flowing in the solenoid = 1 A
- Relative permeability of the inside material = 1000
To find: Energy per unit length of solenoid
Solution:
Step 1: Calculate the magnetic field inside the solenoid
- Magnetic field inside the solenoid is given by B = μ₀nI, where μ₀ is the permeability of free space, n is the turn density and I is the current
- μ₀ = 4π × 10^-7 Tm/A
- n = 5000 turns/m
- I = 1 A
- B = μ₀nI = 4π × 10^-7 Tm/A × 5000 turns/m × 1 A = 0.002 T
Step 2: Calculate the magnetic flux density inside the solenoid
- Magnetic flux density, B = μH, where H is the magnetic field intensity and μ is the relative permeability
- H = B/μ = 0.002 T/1000 = 2 × 10^-6 T
- Therefore, magnetic flux density inside the solenoid is 2 × 10^-6 T
Step 3: Calculate the energy per unit volume of the magnetic field inside the solenoid
- Energy per unit volume of the magnetic field, u = 1/2μB^2
- u = 1/2 × 4π × 10^-7 Tm/A × (0.002 T)^2 = 1.256 × 10^-9 J/m^3
Step 4: Calculate the energy per unit length of the solenoid
- Energy per unit length of the solenoid, U = uAL
- A = 0.001 m^2 (given)
- L = 1 m (as we are calculating energy per unit length)
- Therefore, U = 1.256 × 10^-9 J/m^3 × 0.001 m^2 × 1 m = 1.256 × 10^-12 J/m
Answer: The energy per unit length of the solenoid is 1.256 × 10^-12 J/m.
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A solenoid has turn density 5000 turn/m and cross sectional area 10 cm...
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A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.?
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A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.?.
A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solenoid has turn density 5000 turn/m and cross sectional area 10 cm^2 .If a current of 1A flow in it and inside material has relative permeability of 1000 then find energy per unit length of solenoid.?.
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