Singly ionized (one electron removed) atoms are accelerated...

Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting of perpendicular electric and magnetic fields. The electric field is 155 $\mathrm{V} / \mathrm{m}$ and the magnetic field is 0.0315 T. The ions next enter a uniform magnetic field of magnitude 0.0175 $\mathrm{T}$ that is oriented perpendicular to their velocity. (a) How fast are the ions moving when they emerge from the velocity selector? (b) If the radius of the path of the ions in the second magnetic field is $17.5 \mathrm{cm},$ what is their mass?

Key Concepts

Velocity Selector

A velocity selector is a device that employs perpendicular electric and magnetic fields to allow particles with a specific velocity to pass through undeflected. When the electric force (qE) balances the magnetic force (qvB), only particles with velocity v = E/B experience zero net force, ensuring that only those particles continue in a straight path downstream.

Charged Particle Motion in a Magnetic Field

When a charged particle enters a uniform magnetic field perpendicular to its velocity, it experiences the Lorentz force, which acts as a centripetal force that continuously changes the direction of the particle's velocity. This causes the particle to follow a circular path, with the radius of curvature determined by the particle's mass, velocity, charge, and the strength of the magnetic field.

Centripetal Force in Circular Motion

In circular motion, the centripetal force required to keep a particle moving in a circle is provided by the magnetic force on a charged particle. The balance of this force, given by qvB, with the required centripetal force, m(v^2)/r, allows one to derive relationships between the particle's mass, velocity, magnetic field strength, and the radius of the circular path.

Singly Ionized Atoms

Singly ionized atoms have lost one electron, which results in a net charge equal to the elementary charge (e). This property is crucial in calculations involving electromagnetic forces, as the known charge value simplifies determining the forces acting on the ion in electric and magnetic fields.

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