Final answer:
To calculate the value of direct current needed in a coil of 1000 turns uniformly wound round the ring to create a flux of 0.5 mWb in the air gap, we can use the formula: magnetic field strength = (magnetic flux) / (cross-sectional area). By substituting the given values and using the appropriate formulas, we can find the value of the current needed.
Step-by-step explanation:
To calculate the value of direct current needed in a coil of 1000 turns uniformly wound round the ring to create a flux of 0.5 mWb in the air gap, we can use the formula:
magnetic flux = magnetic field strength x cross-sectional area
First, we need to calculate the magnetic field strength using the formula:
magnetic field strength = (magnetic flux) / (cross-sectional area)
The cross-sectional area of the ring is given as 3.6 cm² which is equal to 3.6 x 10⁻⁴ m². So, the magnetic field strength is:
magnetic field strength = (0.5 x 10⁻³ Wb) / (3.6 x 10⁻⁴ m²)
Next, we can calculate the current needed to create this magnetic field strength using the formula:
current = (magnetic field strength) / (number of turns)
Given that the air gap is 1 mm wide and the relative permeability for iron is 650, we can use the formula:
magnetic field strength = (u₀ x current) / (2π x air gap)
By substituting the values into the formula, we can solve for the current:
current = (2π x air gap x magnetic field strength) / (u₀)
Where u₀ is the permeability of free space (4π x 10⁻⁷ Tm/A).
Finally, we can substitute the values and calculate the current needed:
current = (2π x 0.001 m x magnetic field strength) / (650 x 4π x 10⁻⁷ Tm/A)
By simplifying the equation, we can find the value of the current needed.