⚡ Magnetic Circuits & Solenoid Design
Magnetomotive Force ($\text{MMF}$) Converter
Convert magnetic potential driving force ($\mathcal{F} = N \cdot I$) across Ampere-turns ($\text{At}$), $\text{Gilberts}$ ($\text{Gb}$), Kiloampere-turns ($\text{kAt}$), and $\text{Amperes}$.
📦 PCB Relay (10 At)
⚡ Contactor (1,000 At)
🧲 Lifting Magnet (50 kAt)
🏥 MRI Magnet (2 MAt)
Input MMF Value
Standard Gilberts (Gb)
1,256.64 Gb
Ampere-turns
1,000 At
kAt
1.000 kAt
Gilberts (Gb)
1,257 Gb
💡 Hopkinson's Law for Magnetic Circuits:
$$\mathcal{F} = \Phi \cdot \mathcal{R} \implies 1\text{ At} = \frac{4\pi}{10}\text{ Gb} \approx 1.25664\text{ Gilberts}$$
Understanding Magnetomotive Force (MMF)
Magnetomotive force ($\mathcal{F}$) is the driving potential that establishes magnetic flux in a magnetic circuit, analogous to electromotive force (voltage) in an electric circuit:
- Solenoid Coil: $$\mathcal{F} = N \cdot I \text{ (Number of Turns } \times \text{ Current)}$$
- Hopkinson's Law (Magnetic Ohm's Law): $$\mathcal{F} = \Phi \cdot \mathcal{R}_{\text{mag}}$$ ($\Phi = \text{magnetic flux}$, $\mathcal{R}_{\text{mag}} = \text{magnetic reluctance}$).
- Gilbert vs Ampere-turn: The Gilbert is the CGS unit, defined as $1\text{ Gb} = \frac{10}{4\pi}\text{ At} \approx 0.795775\text{ At}$.