calculate the relative permeability of an iron ring when the exiting current taken by the 600-turns of coils is 1.2A and the total flux produce is 1mwb.the mean circumference of the rings is 50m and the area of the cross section is 10cm^2?...
To calculate the relative permeability of an iron ring, we need to use the equation:
μr = (μ0 * N * I) / (Φ * A),
where:
- μr is the relative permeability,
- μ0 is the permeability of free space (constant, approximately equal to 4π x 10^-7 T•m/A),
- N is the number of turns of the coils (600 turns),
- I is the current passing through the coils (1.2A),
- Φ is the total magnetic flux produced (1mWb), and
- A is the cross-sectional area of the iron ring (in this case, 10cm^2).
First, let's convert the given values to the appropriate units:
- The mean circumference of the ring is given as 50m.
- The area of the cross-section is given as 10cm^2.
Next, we'll convert the measurements:
- Convert the mean circumference of the ring from meters to centimeters: 50m * 100cm/m = 5000cm.
- Convert the cross-sectional area from cm^2 to m^2: 10cm^2 * (1m/100cm)^2 = 0.01m^2.
Now we can substitute these values into the formula:
μr = (4π x 10^-7 T•m/A) * (600 turns) * (1.2 A) / (1 mWb * 0.01m^2).
Calculating the expression:
μr = (4π x 10^-7 * 600 * 1.2) / (1 * 0.01).
Simplifying:
μr = (4π x 10^-7 * 600 * 1.2) / 0.01.
μr = (4 * 3.14159 * 10^-7 * 600 * 1.2) / 0.01.
μr ≈ 0.905.
Therefore, the relative permeability of the iron ring in this scenario is approximately 0.905.