16. A current of 2A passes through a coil of 350 turn wound on a ring of mean diameter 12cm. The flux density established in the ring is 1.4 Wb/m2. Find the value of relative permeability of iron?

Question

Answer

Calculation of Relative Permeability of Iron

Given:

Current through coil, I = 2A

Number of turns in coil, N = 350

Mean diameter of ring, d = 12 cm

Flux density in ring, B = 1.4 Wb/m²

Formula:

Magnetic field intensity, H = (N * I) / l

Magnetic field strength, B = μ * μ_o * H

Flux density in ring, B = Φ / A

Area of cross-section of ring, A = π * d² / 4

Permeability of free space, μ_o = 4π * 10^-7 H/m

Relative permeability of iron, μ = B / (μ_o * H)

Solution:

Length of ring, l = π * d = π * 12 cm = 37.7 cm = 0.377 m

Magnetic field intensity, H = (350 * 2) / 0.377 = 1852.96 A/m

Area of cross-section of ring, A = π * 12² / 4 = 113.1 cm² = 0.01131 m²

Magnetic field strength, B = 1.4 * 10^-3 T (1 T = 1 Wb/m²)

Permeability of free space, μ_o = 4π * 10^-7 H/m

Relative permeability of iron, μ = B / (μ_o * H) = 1.4 * 10^-3 / (4π * 10^-7 * 1852.96) = 728.7

Explanation:

The given problem can be solved using the formula for magnetic field intensity, magnetic field strength, flux density, area of cross-section of the ring, permeability of free space, and relative permeability of iron. Firstly, we calculated the magnetic field intensity using the formula (N * I) / l. Then, we calculated the area of cross-section of the ring using the formula π * d² / 4. After that, we calculated the magnetic field strength using the formula μ * μ_o * H and flux density using the formula Φ / A. Later, we calculated the relative permeability of iron using the formula B / (μ_o * H). The relative permeability of iron is 728.7.

Similar Electrical Engineering (EE) Doubts

A current of 2 A passes through a coil of 350 turn wound on a ring of mean diameter 12 cm. The flux density established in the ring is 1.4 wb/m². Find the value of relative permeability of iron. (kr 191 (B) 600 (C) 1200 (D) 210x103?

An iron ring with mean length of 60cm is uniformly wound with 250 turns of wire . Calculate the value of Flux density if a current of 2A flows through a wire . Assume relative permeability 500 for iron?

An iron ring of mean circumference of 50 cm has an air gap of 2mm cut in it. It has circular cross section with area of 5cm2 . It carries a coil wound with 600 turns uniformly. The relative permeability of iron is 580. If coil carries a current of 2 A find flux in air gap.?

A coil is wound uniformly with 300 turns over a steel ring of relative permeability 900 having a mean circumference of 400nm and cross sectional area of 500mm^2 if a current of 25A is passed through the cool find MMF, reluctance and flux?

Top Courses for Electrical Engineering (EE)View all

Network Theory (Electric Circuits)

GATE Electrical Engineering (EE) Mock Test Series 2025

General Aptitude for GATE

GATE Notes & Videos for Electrical Engineering

Engineering Mathematics

Top Courses for Electrical Engineering (EE)

Top Courses for Electrical Engineering (EE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company