AcademyMagnetic Fields and Forces
Academy
Particle Motion Applications
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
Magnetic and electric fields select, separate, or measure charged particles by force balance.
Notation
\(E\)
electric field magnitude
\(\mathrm{N\,C^{-1}}\)
\(B\)
magnetic field magnitude
\(\mathrm{T}\)
\(v\)
particle speed
\(\mathrm{m\,s^{-1}}\)
\(r\)
magnetic-path radius
\(\mathrm{m}\)
\(m/q\)
mass-to-charge ratio
\(\mathrm{kg\,C^{-1}}\)
Method
In crossed fields, electric and magnetic forces can oppose each other. Particles pass undeflected when the magnitudes match.
Electric force
\[F_E=|q|E\]
Magnetic force
\[F_B=|q|vB\]
Velocity selector
\[|q|E=|q|vB\]
Selected speed
\[v=\frac{E}{B}\]
After speed selection, a magnetic analyzer can determine mass-to-charge ratio from the orbit radius.
Magnetic radius
\[r=\frac{mv}{|q|B}\]
Mass-to-charge ratio
\[\frac{m}{|q|}=\frac{rB}{v}\]
Rules
Velocity selector
\[v=\frac{E}{B}\]
Magnetic analyzer
\[\frac{m}{|q|}=\frac{rB}{v}\]
Momentum radius
\[p=|q|Br\]
Examples
Question
A selector has
\[E=2.4\times10^4\,\mathrm{N\,C^{-1}}\]
and \[B=0.12\,\mathrm{T}\]
Find the selected speed.Answer
\[v=\frac{E}{B}=\frac{2.4\times10^4}{0.12}=2.0\times10^5\,\mathrm{m\,s^{-1}}\]
Checks
- A velocity selector chooses speed, not mass directly.
- Opposite charge signs reverse both electric and magnetic forces, so the same speed condition applies.
- In a magnetic analyzer, larger mass-to-charge ratio gives a larger radius.