Lorentz Force Visualizer
Lorentz Force Visualizer calculates and visualizes the force on a charged particle in electric and magnetic fields in 3D.
Formulas Used in Lorentz Force Visualizer
The visualizer computes the Lorentz force on a charged particle in electric and magnetic fields using the following formula:
Lorentz Force:
\\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \\]Components:
\\[ F_x = q E_x + q (v_y B_z – v_z B_y) \\] \\[ F_y = q E_y + q (v_z B_x – v_x B_z) \\] \\[ F_z = q E_z + q (v_x B_y – v_y B_x) \\]Magnitude:
\\[ |\mathbf{F}| = \sqrt{F_x^2 + F_y^2 + F_z^2} \\]Where:
- \\( \mathbf{F} \\): Lorentz force vector (N)
- \\( q \\): Charge of the particle (C)
- \\( \mathbf{E} \\): Electric field vector (N/C)
- \\( \mathbf{v} \\): Velocity vector of the particle (m/s)
- \\( \mathbf{B} \\): Magnetic field vector (T)
- \\( F_x, F_y, F_z \\): Force components (N)
- \\( |\mathbf{F}| \\): Force magnitude (N)
Example Calculations
Example: Particle with \\( q = 1.6 \times 10^{-19} \, \text{C}, \mathbf{v} = (1000, 0, 0) \, \text{m/s}, \mathbf{E} = (100, 0, 0) \, \text{N/C}, \mathbf{B} = (0, 1, 0) \, \text{T} \\)
\\[
F_x = 1.6 \times 10^{-19} \cdot 100 + 1.6 \times 10^{-19} \cdot (0 \cdot 0 – 0 \cdot 1) = 1.6 \times 10^{-17} \, \text{N}
\\]
\\[
F_y = 1.6 \times 10^{-19} \cdot 0 + 1.6 \times 10^{-19} \cdot (0 \cdot 0 – 1000 \cdot 0) = 0 \, \text{N}
\\]
\\[
F_z = 1.6 \times 10^{-19} \cdot 0 + 1.6 \times 10^{-19} \cdot (1000 \cdot 1 – 0 \cdot 0) = 1.6 \times 10^{-16} \, \text{N}
\\]
\\[
|\mathbf{F}| = \sqrt{(1.6 \times 10^{-17})^2 + 0^2 + (1.6 \times 10^{-16})^2} \approx 1.61 \times 10^{-16} \, \text{N}
\\]
Result: \\( \mathbf{F} \approx (1.6 \times 10^{-17}, 0, 1.6 \times 10^{-16}) \, \text{N}, |\mathbf{F}| \approx 1.61 \times 10^{-16} \, \text{N} \\)