Solenoid Coil Electromagnetic Force Calculator

Solenoid Magnetic Force Estimator

Input Fields

Number of turns

N

Total number of turns in the coil

Current

I

A

Current through the coil

Core area

A

cm²

Cross-sectional area of core (cm²)

Air gap

g

mm

Gap between core and armature (mm)

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Your Results

Electromagnetic Force

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Solenoid Electromagnetic Force Formula

$$F = \frac{{B^2 \cdot A}}{{2 \cdot \mu_0}}$$ $$B = \mu_0 \cdot \mu_r \cdot \frac{{N \cdot I}}{L}$$

Where:

• $$F$$ = electromagnetic force (N)
• $$B$$ = magnetic flux density (T)
• $$A$$ = cross-sectional area of the core (m²)
• $$N$$ = number of turns
• $$I$$ = current (A)
• $$L$$ = length of coil (m)
• $$\mu_0$$ = permeability of free space $$≈ 4\pi

These formulas assume a uniform magnetic field and cylindrical geometry.

Solenoid Coil Electromagnetic Force – Calculation Example

Given:

• $$N$$ = 1000 turns
• $$I$$ = 2 A
• $$L$$ = 0.1 m
• $$A$$ = 0.0002 m²
• $$\mu_r$$ = 1000

Calculation:

1. $$B = 4\pi \cdot 10^{-7} \cdot 1000 \cdot \frac{1000 \cdot 2}{0.1} ≈ 0.0251~\text{T}$$
2. $$F = \frac{(0.0251)^2 \cdot 0.0002}{2 \cdot 4\pi \cdot 10^{-7}} ≈ \frac{1.26 \cdot 10^{-7}}{2.513 \cdot 10^{-6}} ≈ 0.0501~\text{N}$$

Solenoid coils are used in countless electromagnetic devices to convert electrical energy into mechanical motion. This calculator helps engineers and students predict the magnetic pulling force generated by a solenoid under certain current and geometric conditions. It’s particularly useful in applications involving magnetic actuators, electromagnetic locks, and robotic grippers.