Magnetic Force By Lorentz Force Equation Calculator

Lorentz Force Equation:

\[ F_{mag} = Q \times (E + (\nu \times B \times \sin(\theta))) \]

Charge of Particle (Q):

Electric Field (E):

V/m

Speed of Charged Particle (ν):

m/s

Magnetic Flux Density (B):

Incidence Angle (θ):

Magnetic Force (F_mag):

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1. What is the Lorentz Force Equation?

The Lorentz Force Equation describes the force exerted on a charged particle moving through electric and magnetic fields. It combines both electric and magnetic components of the electromagnetic force acting on the particle.

2. How Does the Calculator Work?

The calculator uses the Lorentz Force Equation:

\[ F_{mag} = Q \times (E + (\nu \times B \times \sin(\theta))) \]

Where:

\( F_{mag} \) — Magnetic force (N)
\( Q \) — Charge of particle (C)
\( E \) — Electric field (V/m)
\( \nu \) — Speed of charged particle (m/s)
\( B \) — Magnetic flux density (T)
\( \theta \) — Incidence angle between velocity and magnetic field vectors (°)

Explanation: The equation calculates the total electromagnetic force on a charged particle, accounting for both electric field effects and the magnetic force component that depends on the particle's velocity and the angle between velocity and magnetic field.

3. Importance of Magnetic Force Calculation

Details: Accurate calculation of magnetic force is crucial for understanding charged particle motion in electromagnetic fields, designing particle accelerators, analyzing plasma physics, and developing electromagnetic devices.

4. Using the Calculator

Tips: Enter charge in coulombs, electric field in volts per meter, speed in meters per second, magnetic flux density in tesla, and incidence angle in degrees. All values must be valid (charge ≠ 0, speed ≥ 0, angle between 0-180°).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the sine function in the equation?
A: The sin(θ) term accounts for the fact that the magnetic force is maximum when the particle moves perpendicular to the magnetic field (θ = 90°) and zero when moving parallel to it (θ = 0° or 180°).

Q2: Can this equation handle negative charges?
A: Yes, negative charge values will result in a force opposite to what would be experienced by a positive charge with the same magnitude.

Q3: What happens when the electric field is zero?
A: When E = 0, the equation reduces to the magnetic force component only: F = Q(ν × B × sin(θ)).

Q4: How does the angle affect the magnetic force?
A: The magnetic force is proportional to sin(θ), reaching maximum at 90° and minimum at 0° and 180°.

Q5: What are typical units for these measurements?
A: Charge in coulombs (C), electric field in volts per meter (V/m), speed in meters per second (m/s), magnetic flux density in tesla (T), and force in newtons (N).