Our orders are delivered strictly on time without delay
An electromagnet in the form of a U shape has an air gap, between each pole and an
armature, of 0.05 cm. The cross sectional area of the magnetic core is 5 cm2 and it is uniformly
wound with 100 turns. Neglecting leakage and fringing flux, calculate the current necessary to
give a force of 147.2 N on the armature. Assume 15% of the total mmf is expended on the iron
part of the magnetic circuit.
where:
F is the force in NewtonsN is the number of turns of the coilI is the current in Amperesμ₀ is the permeability of free space (4π × 10^-7 T·m/A)A is the cross-sectional area of the coreg is the air gap distanceCalculating the Effective Magnetomotive Force (MMF):
Given that 15% of the total MMF is expended on the iron part, 85% is available for the air gap.
MMF_air_gap = 0.85 * N * I
Relating MMF to Magnetic Field Intensity (H):
For the air gap:
H = MMF_air_gap / (2 * g)
Relating Magnetic Field Intensity to Magnetic Flux Density (B):
B = μ₀ * H
Relating Magnetic Flux Density to Force:
The force on the armature is given by:
F = (B^2 * A) / (2 * μ₀)
Combining Equations and Solving for I:
By substituting the expressions for B and H into the force equation and rearranging, we can solve for the current I.
Note: To simplify the calculations, we can combine the equations and directly solve for I in terms of the given parameters.
After calculating the required current, it's essential to consider the practical limitations of the electromagnet, such as the maximum current capacity of the wire and the power supply.
Understanding the Problem:
We're given a U-shaped electromagnet with specific dimensions and a desired force output. The challenge is to determine the necessary current to achieve this force.
Key Formula:
The force exerted by an electromagnet can be calculated using the following formula:
F = (N * I)^2 * μ₀ * A / (2 * g^2)