A magnetic circuit shown in Fig. 5 has an iron core with a relative permeability of 1000and a 500 turn coil wound on the iron core. Find the current i in the exciting coilrequired to establish a flux of 100µWb in the air gap

To find the current i in the exciting coil required to establish a flux of 100µWb in the air gap, we can use the formula for magnetic flux:

Φ = N * B * A

Where: Φ is the magnetic flux (in Weber), N is the number of turns in the coil, B is the magnetic field strength (in Tesla), A is the cross-sectional area of the air gap (in square meters).

In this case, we are given that the flux Φ is 100µWb, the number of turns N is 500, and we need to find the current i.

First, we need to find the magnetic field strength B. We can use the formula:

B = μ * H

Where: B is the magnetic field strength (in Tesla), μ is the permeability of the material (in Henrys per meter), H is the magnetic field intensity (in Ampere-turns per meter).

Given that the relative permeability of the iron core is 1000, we can calculate the permeability μ:

μ = μ0 * μr

Where: μ0 is the permeability of free space (4π * 10^-7 H/m), μr is the relative permeability of the material.

Substituting the values, we get:

μ = (4π * 10^-7 H/m) * 1000 = 4π * 10^-4 H/m

Now, we can find the magnetic field intensity H using the formula:

H = N * i

Where: H is the magnetic field intensity (in Ampere-turns per meter), N is the number of turns in the coil, i is the current in the coil (in Amperes).

Substituting the values, we get:

H = 500 * i

Finally, we can substitute the values of μ and H into the formula for B:

B = μ * H = (4π * 10^-4 H/m) * (500 * i) = 2π * 10^-1 * i H/m

Now, we can substitute the values of B, Φ, and A into the formula for magnetic flux to solve for i:

Φ = N * B * A

100µWb = 500 * (2π * 10^-1 * i) * A

Simplifying the equation, we get:

i = (100µWb) / (500 * 2π * 10^-1 * A)

Please note that the cross-sectional area A of the air gap is not provided in the given information. You will need to know the value of A in order to calculate the current i.