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A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core?
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A solenoid has 10^3 turns per unit length. On passing a current of 2A,...
**Calculation of Magnetic Susceptibility of Core**
**Given Data:**
- Number of turns per unit length of the solenoid (N) = 10^3 turns/m
- Current passing through the solenoid (I) = 2A
- Magnetic induction (B) = 4π Wb/m^2
**Formula:**
The magnetic field inside a solenoid is given by the equation:
B = μ₀ * μᵣ * N * I
where:
- B is the magnetic field in Tesla (T)
- μ₀ is the permeability of free space (4π * 10^-7 Tm/A)
- μᵣ is the relative permeability of the core material
- N is the number of turns per unit length of the solenoid
- I is the current passing through the solenoid
The relative permeability (μᵣ) of the core material is related to the magnetic susceptibility (χ) by the equation:
μᵣ = 1 + χ
**Calculation:**
1. Rearranging the equation B = μ₀ * μᵣ * N * I, we can solve for μᵣ:
μᵣ = B / (μ₀ * N * I)
= (4π Wb/m^2) / (4π * 10^-7 Tm/A * 10^3 turns/m * 2A)
= (4π / 4π) * (Wb/m^2 / Tm/A * turns/m * A)
= (Wb / T)
= T^-1
2. Substituting the value of μᵣ into the equation μᵣ = 1 + χ, we can solve for χ:
χ = μᵣ - 1
= (T^-1) - 1
= -1
**Answer:**
The magnetic susceptibility (χ) of the core is -1.
**Given Data:**
- Number of turns per unit length of the solenoid (N) = 10^3 turns/m
- Current passing through the solenoid (I) = 2A
- Magnetic induction (B) = 4π Wb/m^2
**Formula:**
The magnetic field inside a solenoid is given by the equation:
B = μ₀ * μᵣ * N * I
where:
- B is the magnetic field in Tesla (T)
- μ₀ is the permeability of free space (4π * 10^-7 Tm/A)
- μᵣ is the relative permeability of the core material
- N is the number of turns per unit length of the solenoid
- I is the current passing through the solenoid
The relative permeability (μᵣ) of the core material is related to the magnetic susceptibility (χ) by the equation:
μᵣ = 1 + χ
**Calculation:**
1. Rearranging the equation B = μ₀ * μᵣ * N * I, we can solve for μᵣ:
μᵣ = B / (μ₀ * N * I)
= (4π Wb/m^2) / (4π * 10^-7 Tm/A * 10^3 turns/m * 2A)
= (4π / 4π) * (Wb/m^2 / Tm/A * turns/m * A)
= (Wb / T)
= T^-1
2. Substituting the value of μᵣ into the equation μᵣ = 1 + χ, we can solve for χ:
χ = μᵣ - 1
= (T^-1) - 1
= -1
**Answer:**
The magnetic susceptibility (χ) of the core is -1.
Community Answer
A solenoid has 10^3 turns per unit length. On passing a current of 2A,...
We know that,
B=u(H+M). & X=M/H
Given, B=4π Wbm^-2
Therefore,
4π=4π*10^-7 * (1+X)
10^7=1+X
Therefore, 10^7-1 = X
X~10^7
B=u(H+M). & X=M/H
Given, B=4π Wbm^-2
Therefore,
4π=4π*10^-7 * (1+X)
10^7=1+X
Therefore, 10^7-1 = X
X~10^7
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A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core?
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A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core?.
A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solenoid has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be 4πWb/m^2. Calculate magnetic susceptibility of core?.
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