Question

A solenoid has a core of material with relative permeability 200. The windings of the solenoid are insulated from the core and carry a current of 1A. If the number of turns is 2000 per metre, calculate

1. magnetic intensity,
2. magnetic field and
3. magnetisation.

Answer 1

Given:

Relative permeability (μ_r) = 200

Current (I) = 1 A

Number of turns per metre (n) = 2000 turns/m

Magnetic constant (μ₀) = 4π × 10⁻⁷ H/m

A. Magnetic intensity:

H = nI

= 2000 × 1

= 2000 A/m

= 2 × 10³ A/m

B. Magnetic field:

B = μ₀μ_rH

= 4π × 10⁻⁷ × 200 × 2 × 10³

= (4 × 200 × 2) × (π × 10⁻⁷ × 10³) T

= 1600 × (π × 10⁻⁷⁺³) T

= 1600 × (π × 10⁻⁴) T

= 1.6 × 10³ × π × 10⁻⁴ T

= 1.6π × 10³⁻⁴ T

= 1.6π × 10⁻¹ T

= 0.16π T

= 0.16 × 3.14159 T ...(π = 3.14159)

= 0.50265 T

= 0.50 T

C. Magnetisation:

M = (μ_r − 1)H

= (200 − 1) × 2000 A/m

= 199 × 2000 A/m

= 398000 A/m

= 3.98 × 10⁵ A/m