QuickField : magnetostatics examples

Inductance of a trace on a pcb

A circular trace of a pcb is specified by its thickness (35 μm) width (2 mm) and radius (4 mm).

  What is its inductance @ 1 kHz ?

  Compare with the Quickfield Pro answer (about. 4000 nodes)
  to deduce that the found value must divided by 2.

  Answer : L = 13.5 nH

   Download Student's Quickfield files (about 180 nodes)  (8 Ko)

   Download Pro Quickfield files (about 4000 nodes)  (155 Ko)

Description

pcb trace

Validity of long solenoid formula

The inductance value of a long solenoid is given by :

Its diameter is 70 mm his length 22 mm, 21 turns of 0.5mm radius.

  From which frequency is the above formula no more valid ?

  Réponse : 1400 nodes" ⇒ 0.97 μH and "190 nodes" ⇒ 0.88 μH @ 50 Hz. The magnetic flux decreases for f > 100 kHz.

   Download Student's Quickfield files (about 190 nodes)   (11 Ko)

   Download Pro Quickfield files (about 1400 nodes)   (60 Ko)

Description

Solenoid design

Description

inductance plot

Eddy currents in a cable

The document UTE C 15-421 (Low-voltage electrical installations Installations supplies in alternating current with nominal frequency between 100 to 400 Hz) states that a conductor made of copper (cross section 100 mm²) at 400 Hz has a skin depth of 3.4 mm. For a cross section of 95 mm² this document proposes a reduction coefficient of 0.85 on allowed current

  Check these data.

  skin depth = δ = √(2ρ/μ₀ω) with ρ = 1.85e^-8Ω.m and ω = 2πf
  Draw a contour to watch the shape of the current density and calculate the values "total current" and "external current" on the conductor section.

  The idea to have only a peripheral current is wrong. The skin depth gives an indication on the decrease of the current density.

  Answer : The "itotal" current density curve becomes smooth close to 3.5 mm

  Answer : For the simulation, a current density of 10 A/mm² has been chosen, giving 1000 A ⇒ 1000/1137 = 0.88

   Student (about 180 nodes)  (8 Ko).

   Pro (about 4000 nodes)  (156 Ko).

Description

Eddy current in a cable