Question

In the Bainbridge mass spectrometer, the magnetic-field magnitude in the velocity selector is 0.650 T, and ions having a speed of 1.82 x 10^6 m/s pass through undeflected (a) What is the electric-field magnitude in the velocity selector? (b) If the separation of the plates is 5.20 mm, what is the potential difference between plates P and P"?

Answer 1

(a) By the definition of the Lorentz force law we have:

$$F=qE-qvB.$$

Since we have a zero deflection, the net force $F$ will be equal to zero, so we get:

$$0=qE-qvB,$$ $$E=vB=1.82\cdot10^6\ \dfrac{m}{s}\cdot0.650 T=1.18\cdot10^6\ \dfrac{V}{m}.$$

(b) We can find the potential difference between plates P and P" as follows:

$$V=Ed=1.18\cdot10^6\ \dfrac{V}{m}\cdot5.2\cdot10^{-3}\ m=6136\ V.$$