Formula: Specific Charge of a particle in a Magnetic Field Electric charge Mass Acceleration voltage Magnetic flux density (B-field) Radius
$$\frac{q}{\class{brown}{m}} ~=~ \frac{2 \, U_{\text B}}{r^2 \, \class{violet}{B}^2}$$
$$q ~=~ \frac{2 \, \class{brown}{m} \, U_{\text B}}{r^2 \, \class{violet}{B}^2}$$
$$\class{brown}{m} ~=~ \frac{q \, r^2 \, \class{violet}{B}^2}{2 \, U_{\text B}}$$
$$U_{\text B} ~=~ \frac{q \, r^2 \, \class{violet}{B}^2}{2\class{brown}{m}}$$
$$\class{violet}{B} ~=~ \frac{1}{r} \sqrt{\frac{2 \, \class{brown}{m} \, U_{\text B}}{q}}$$
$$r ~=~ \frac{1}{\class{violet}{B}} \, \sqrt{ \frac{2 \, \class{brown}{m} \, U_{\text B}}{q} }$$
Electric charge
$$ q $$ Unit $$ \mathrm{C} = \mathrm{As} $$
Electric charge of the particle (e.g. electron) moving on a circular path in a magnetic field.
The ratio of the charge \(q\) to the mass \(m\) of the particle is called specific charge \( \frac{q}{m} \). For example, the electron has the following specific charge: \( \frac{q}{m} = - 1.758 \cdot 10^{11} \, \frac{\text C}{\text{kg} } \).
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the particle.
- If the particle is a electron, then the mass is \( m = 9.1 \cdot 10^{-31} \, \text{kg} \).
- If the particle is a proton, then the mass is \( m = 1.67 \cdot 10^{-27} \, \text{kg} \).
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Acceleration voltage
$$ U_{\text B} $$ Unit $$ \mathrm{V} $$
Accelerating voltage set, for example, in the electron gun in the teltron tube experiment to change the velocity of electrons or other charged particles.
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$
Magnetic flux density describes how strong the magnetic field is in which the charged particle moves.
Radius
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the circular path on which the charged particle moves. By changing the magnetic field \(\class{violet}{B}\) you can easily make the radius \(r\) of the circular path larger or smaller.