Lorentz Force Law (Total)

📊 advanced

$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$

The total force acting on a point charge moving through both electric and magnetic fields.

Variables & Units

$\vec{E}$

Electric field vector

Unit: $V/m$ or $N/C$

$\vec{B}$

Magnetic field vector

Unit: Tesla ($T$)

$\vec{v}$

Velocity vector

Unit: $m/s$

Key Information

📐 Derived From

Combination of electrostatic and magnetic force observations.

💡 Example

Helical path of a proton in a uniform magnetic and electric field.

🔧 Applications

Mass spectrometry, cyclotrons, and plasma physics.

⚠️ Constraints

Point charge.

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