Hopkinson’s Law (Magnetic Ohm’s Law)

Φ = F / S

Quick answer

This calculator solves Φ = F / S (flux = MMF / reluctance) for Magnetic Flux. With MMF 1 kA·t, Reluctance 1 MA·t/Wb, the result is 1 mWb. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Magnetic Flux (mWb)
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Formula

Φ = F / S (flux = MMF / reluctance)

Description

Hopkinson’s law is the magnetic equivalent of Ohm’s law: magnetic flux equals magnetomotive force divided by reluctance, exactly as current equals voltage divided by resistance. It lets a magnetic circuit be analysed with the same techniques as an electric one—series and parallel reluctances, source MMFs, and flux division.

Variables

  • Φ — Magnetic flux (weber)
  • F — Magnetomotive force (ampere-turns)
  • S — Reluctance (ampere-turns/weber)

Practical Notes

Unlike electric current, magnetic flux dissipates no power flowing through reluctance—reluctance stores rather than dissipates energy. The analogy breaks down at saturation, where µr and hence reluctance become flux-dependent.

Symbols and units

Symbol Meaning Default unit Accepted units
phi Magnetic Flux mWb µWb, mWb, Wb
F MMF A·t A·t, kA·t
S Reluctance A·t/Wb A·t/Wb, kA·t/Wb, MA·t/Wb

Step by step

  1. 1. What you know: MMF 1 kA·t, Reluctance 1 MA·t/Wb
  2. 2. The relation: Φ = F / S (flux = MMF / reluctance)
  3. 3. Substitute: F = 1 kA·t, S = 1 MA·t/Wb
  4. 4. Result: Magnetic Flux = 1 mWb

Worked examples

Minimum range

Given: MMF 10 A·t, Reluctance 10 kA·t/Wb

Result: Magnetic Flux = 1 mWb

Low range

Given: MMF 100 A·t, Reluctance 100 kA·t/Wb

Result: Magnetic Flux = 1 mWb

Typical

Given: MMF 1 kA·t, Reluctance 1 MA·t/Wb

Result: Magnetic Flux = 1 mWb

High range

Given: MMF 10 kA·t, Reluctance 10 MA·t/Wb

Result: Magnetic Flux = 1 mWb

Maximum range

Given: MMF 100 kA·t, Reluctance 100 MA·t/Wb

Result: Magnetic Flux = 1 mWb

Solving for each variable

Solve for Magnetic Flux

MMF 10 A·t, Reluctance 10 kA·t/Wb → 1 mWb

Solve for MMF

Magnetic Flux 100 µWb, Reluctance 10 kA·t/Wb → 1 A·t

Solve for Reluctance

Magnetic Flux 100 µWb, MMF 10 A·t → 100 kA·t/Wb

How Magnetic Flux changes with MMF

MMF (input) Magnetic Flux (result)
100 A·t 100 µWb
0.25 kA·t 0.25 mWb
0.5 kA·t 0.5 mWb
0.75 kA·t 0.75 mWb
1 kA·t 1 mWb
1.5 kA·t 1.5 mWb
2 kA·t 2 mWb
4 kA·t 4 mWb
7 kA·t 7 mWb
10 kA·t 10 mWb

The same result in other units

Unit Value
µWb 1000
mWb 1
Wb 0.001

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Frequently asked questions

How do you calculate Hopkinson’s Law (Magnetic Ohm’s Law)?

Use Φ = F / S (flux = MMF / reluctance). With MMF 1 kA·t, Reluctance 1 MA·t/Wb, Magnetic Flux works out to 1 mWb.

What is the formula for Hopkinson’s Law (Magnetic Ohm’s Law)?

The formula is Φ = F / S (flux = MMF / reluctance). Hopkinson’s law is the magnetic equivalent of Ohm’s law: magnetic flux equals magnetomotive force divided by reluctance, exactly as current equals voltage divided by resistance.

How do you find MMF when you know the other values?

Rearrange for MMF: with Magnetic Flux 100 µWb, Reluctance 10 kA·t/Wb, MMF is 1 A·t.

How do you find Reluctance when you know the other values?

Rearrange for Reluctance: with Magnetic Flux 100 µWb, MMF 10 A·t, Reluctance is 100 kA·t/Wb.

What units does Hopkinson’s Law (Magnetic Ohm’s Law) use?

Magnetic Flux is shown in µWb, mWb, Wb. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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