In the Bainbridge mass spectrometer (see Fig. 27.24 ), the...

In the Bainbridge mass spectrometer (see Fig. 27.24 ), the magnetic-field magnitude in the velocity selector is $0.650 \mathrm{T},$ and ions having a speed of $1.82 \times 10^{6} \mathrm{m} / \mathrm{s}$ pass through undeflected. (a) What is the electric-field magnitude in the velocity selector? (b) If the separation of the plates is $5.20 \mathrm{mm},$ what is the potential difference between plates $P$ and $P^{\prime} ?$

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Key Concepts

Lorentz Force

The Lorentz force is the combined force experienced by a charged particle moving through electric and magnetic fields, given by F = q(E + v × B). In contexts like the velocity selector, the condition that the net force is zero (qE = qvB) allows for precise selection of velocities, making the Lorentz force concept fundamental to the operation of devices in mass spectrometry.

Velocity Selector

A velocity selector is a device that employs mutually perpendicular electric and magnetic fields to allow only particles with a specific velocity to pass through undeflected. This happens when the electric force (qE) exactly cancels the magnetic force (qvB), leading to the condition v = E/B, which serves as the fundamental principle for filtering charged particles by speed.

Electric Field and Potential Difference

In a uniform electric field, the potential difference between two points is directly related to the field strength and the distance between those points by the relation ?V = E · d. This relationship is crucial in determining the voltage applied across components such as the plates in a velocity selector or similar devices.

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