Lorentz Force Calculator: Magnetic and Electric Force on a Charge, Circular Path Radius and Cyclotron Frequency
Find the force on a charged particle or a wire in electric and magnetic fields, and the circle a particle follows.
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How this calculator works
For a particle enter its charge as a multiple of the elementary charge, its mass in atomic mass units, its speed, the magnetic field, any electric field, and the angle between the velocity and the field.
The calculator gives the magnetic and the electric force, the radius of the circular path from m v over q B, the cyclotron frequency and period and the kinetic energy.
For a wire enter the current, the length in the field and the angle. It gives the force and the force for each metre.
Formulas used
- \vec{F} = q(\vec{E} + \vec{v}\times\vec{B})
- F_B = |q|vB\sin\theta
- r = \frac{mv}{|q|B}
- f_c = \frac{|q|B}{2\pi m}
- \vec{F} = I\vec{L}\times\vec{B}
Worked example
With the default numbers in the calculator above:
- Magnetic force on the particle: 1.6022e-14 N
- Radius of the circular path (from the speed at right angles to the field): 104.40 mm (0.10 m)
- Check: magnetic force provides the centripetal force: Both sides equal 1.6022e-14 N
- Cyclotron frequency (it does not depend on the speed): 1.52 MHz
- Period of the circle: 655.95 ns
- Kinetic energy of the particle: 8.3631e-16 J (5.22 keV)
- Power delivered by the magnetic force: None: the magnetic force is always at right angles to the velocity, so it changes the direction but not the speed
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? A current-carrying wire.
- Force on the wire: 0.50 N
- Force for each metre of wire: 1.00 N/m
Common questions
Does the magnetic force do any work?
No. It is always at right angles to the velocity, so it changes the direction of the motion but not the speed or the energy.
Why does the cyclotron frequency not depend on speed?
A faster particle goes round a larger circle, in the same time. The radius grows with the speed and so does the distance.
What is a velocity selector?
Crossed electric and magnetic fields in which only particles of speed E over B go straight through, because the two forces cancel.
When do relativistic effects matter?
Above about a tenth of the speed of light, where the mass appears to increase and these formulas are no longer accurate.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any university physics text (magnetic force on a moving charge); Griffiths, Introduction to Electrodynamics.
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