A flux through a current carrying coil changes from 0.65mwb to 0.91wmb when the air coil is replaced by another material. What are the relative permeability and the permeability of material
To find the relative permeability and permeability of the material, we can use the formula:
μ = B / (μ₀ * I * N)
Where:
- μ is the permeability of the material
- B is the magnetic field strength in Tesla (T)
- μ₀ is the permeability of free space (4π × 10^-7 T m/A)
- I is the current in the coil in Amperes (A)
- N is the number of turns in the coil
First, let's calculate the change in flux (ΔΦ) using the formula:
ΔΦ = Φ₂ - Φ₁
Where:
- ΔΦ is the change in flux in Weber (Wb)
- Φ₂ is the final flux (0.91 Wb)
- Φ₁ is the initial flux (0.65 Wb)
ΔΦ = 0.91 Wb - 0.65 Wb = 0.26 Wb
Next, multiply the change in flux by the number of turns (N) to find the change in magnetic field strength (ΔB):
ΔB = ΔΦ / N
Substitute the values into the equation:
ΔB = 0.26 Wb / N
The relative permeability (μᵣ) can be expressed as:
μᵣ = ΔB / (μ₀ * I)
Substituting the values of ΔB and μ₀:
μᵣ = (0.26 Wb / N) / (4π × 10^-7 T m/A * I)
Now, to find the permeability of the material (μ), we multiply the relative permeability by the permeability of free space:
μ = μᵣ * μ₀
Substituting the values:
μ = (0.26 Wb / N) / (4π × 10^-7 T m/A * I) * (4π × 10^-7 T m/A)
Simplifying the expression:
μ = (0.26) / (I * N)
Therefore, the relative permeability (μᵣ) is equal to 0.26 / (I * N), and the permeability of the material (μ) is equal to 0.26 / (I * N) * (4π × 10^-7 T m/A).