Answer to Question #113322 in Electricity and Magnetism for sabrina

Question

In a mass spectrometer, a particle is ionized to include an additional proton. It is then accelerated to a velocity of 54000 m/s and allowed to enter a magnetic field of 10 T where it is deflected in a semi-circular path with a radius of 2 mm. What is the mass of the particle?

Answer 1

Lorentz force acts on a charge moving in a magnetic field

$F=q \cdot v \cdot B$

The Lorentz force plays the role of a centripetal force, so we can write

$\frac {m_q \cdot v^2}{R}=q \cdot v \cdot B$

Where will we write

$m_q=\frac{q \cdot v \cdot B \cdot R}{v^2}=\frac{q \cdot B \cdot R}{v}=\frac{1.6 \cdot 10^{-19} \cdot 10 \cdot 2 \cdot 10^{-3}}{5.4 \cdot 10^4}=5.926 \cdot 10^{-26}kg$