Simulation · Physics · Class 12

An electron beam in a magnetic field

From the lesson Motion in a magnetic field in Moving Charges and Magnetism. Change the values and watch what happens.

The idea behind it

NCERT §4.3

The magnetic force is always perpendicular to the velocity, so it does no work. The speed and kinetic energy of the charge stay fixed; only the direction of motion changes. An electric force, by contrast, can change the energy.
When v is perpendicular to a uniform B, qvB supplies the centripetal force mv²/r, so the charge moves in a circle of radius r = mv/(qB) in the plane normal to B. More momentum means a bigger circle.
The angular frequency is ω = 2πν = qB/m and the period T = 2πm/(qB). Neither depends on the speed or the energy: a faster charge runs a bigger circle in the same time. ν = qB/2πm is called the cyclotron frequency.
If v has a component v∥ along B, that part is untouched while the perpendicular part still turns in a circle. The path is a helix whose radius uses v⊥ and whose pitch (advance per turn) is p = v∥T = 2πm v∥/(qB).
Example 4.3: an electron (m = 9 × 10⁻³¹ kg) at 3 × 10⁷ m/s in 6 × 10⁻⁴ T moves on a circle of r = mv/(qB) = 0.28 m, at ν = v/2πr ≈ 17 MHz, with energy ½mv² ≈ 4 × 10⁻¹⁶ J ≈ 2.5 keV.
A positive and a negative charge entering the same field with the same velocity curve in opposite senses.

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