Force of Magnetic Field (F=qvb) Calculator

Use this force of magnetic field calculator to calculate Force (F) using magnetic field (B),charge (q),velocity (v) and angle (θ). Force F is given by f=qvbSin(θ)

Force of Magnetic Field (B) Calculator
Magnetic Field (B)
Charge (q)
Velocity (v)
Angle (θ)
Force (F): {{magneticFieldForceResult()}}

How to use Force of Magnetic Field (F=qvb) Calculator?

Step 1 - Enter the Magnetic Field (B)

Step 2 - Enter the Charge (q)

Step 3 - Enter the Velocity (v)

Step 4 - Enter the Angle (θ)

Step 5 - Calculate Magnetic Field Force

Magnetic Field Force Calculator Formula :

F=qvBSin(θ)

Where,

F = Force

B = Magnetic Field

v = Velocity

q = Charge

θ = Angle

Frequently Asked Questions

What is the Lorentz force and how does it affect moving charges in magnetic fields?

The Lorentz force is the fundamental force acting on charged particles moving through magnetic fields: F = qvB sin(θ). This force is always perpendicular to both the velocity and magnetic field, causing the particle to curve rather than accelerate or decelerate. The force is zero when the particle moves parallel to the field (θ = 0°) and maximum when perpendicular (θ = 90°). This force is responsible for particle confinement in plasma, operation of cyclotrons, and bending of charged particle beams.

Why does the Lorentz force depend on the angle between velocity and magnetic field?

The force depends on sin(θ) because only the velocity component perpendicular to B contributes to force: F = q(v_perp)B. When motion is parallel to the field (θ = 0°), there’s no perpendicular component and no force. When perpendicular (θ = 90°), all velocity contributes to force and sin(θ) = 1 (maximum force). This angular dependence is crucial for understanding particle trajectories and designing magnetic confinement systems.

When do charged particles follow circular paths in magnetic fields?

Particles follow circular paths when the Lorentz force provides centripetal acceleration: qvB = mv²/r. This gives circular radius r = mv/(qB). Higher particle velocity increases radius (faster particles less confined), stronger fields decrease radius (tighter confinement). This principle powers cyclotrons (accelerating particles in circular paths) and explains Earth’s magnetosphere confinement of solar wind particles.

How does the Lorentz force differ from electric force on charged particles?

Electric force (F = qE) is parallel or antiparallel to the field and accelerates particles. Magnetic force (F = qvB sin θ) is perpendicular to both field and velocity and deflects particles without changing speed. Electric fields increase or decrease kinetic energy; magnetic fields redirect motion. Combining both fields (as in crossed-field devices) enables velocity selection and particle focusing.

Charged particles falling through magnetic fields experience both gravity and Lorentz deflection. The combination determines the particle trajectory. In planetary atmospheres with magnetic fields, charged particles follow complex helical paths. Understanding this interaction is essential for modeling auroras, cosmic ray propagation, and designing particle detectors.

Physical Basis & References

This calculator applies Lorentz Force Law from Maxwell Equations:

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

For magnetic force only (E = 0): $$F = qvB\sin\theta$$

Key Physics Principles:

  • Lorentz Force - Fundamental electromagnetic force on charges
  • Cross Product - Force perpendicular to both velocity and field
  • Centripetal Motion - Magnetic force provides centripetal acceleration
  • Conservation Laws - Magnetic force preserves kinetic energy

Key Assumptions:

  • Non-relativistic particles (v « c)
  • Uniform magnetic field
  • Point particle (neglecting finite size effects)
  • No self-field effects (particle doesn’t generate significant field)
  • No collisions

Typical Range of Values:

  • Charge: 1 electron (1.6 × 10⁻¹⁹ C) to 1 mC (10⁻³ C)
  • Magnetic field: 0.1 mT to 10 T
  • Velocity: 10⁶ to 10⁸ m/s (various particle regimes)
  • Lorentz force: 10⁻¹⁴ N (electron in weak field) to 10⁻³ N (macroscopic charge in strong field)
  • Particle radius: 1 mm to 10 m (depending on mass and field)

Further Reading:

  • Jackson, J.D. (1998). Classical Electromagnetism, 3rd Edition. Wiley.
  • Goldstein, H. (1980). Classical Mechanics, 2nd Edition. Addison-Wesley.
  • Particle Motion in Electromagnetic Fields - Plasma Physics textbooks

Conclusion

You can read more about Electric Field of Uniformly Charged Disk calculator and Electric Field of Sphere Calculator on below links

Read more about other Physics Calculator on below links