A velocity selector consists of electric and magnetic fields...

A velocity selector consists of electric and magnetic fields described by the expressions $\overrightarrow{\mathbf{E}}=E \hat{\mathbf{k}}$ and $\overrightarrow{\mathbf{B}}=B \hat{\mathbf{j}},$ with $B=15.0 \mathrm{mT} .$ Find the value of $E$ such that $\mathbf{a} 750$ -eV electron moving along the positive $x$ axis is undeflected.

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Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in electric and magnetic fields. It is given by F = q(E + v × B), where q is the charge, E is the electric field, and B is the magnetic field. In the velocity selector, the electric and magnetic components of the Lorentz force are set to cancel each other out for particles moving at the correct speed.

Kinetic Energy to Velocity Conversion

Kinetic energy is related to the speed of a particle through the equation K = ½mv², where m is the mass and v is the velocity of the particle. This conversion is crucial because it allows for the determination of the particle's velocity from its kinetic energy, which in turn is used to set the condition for the electric and magnetic forces to cancel in a velocity selector.

Velocity Selector

A velocity selector is a device that uses perpendicular electric and magnetic fields to allow only charged particles with a specific speed to pass through undeflected. It works by balancing the electric force with the magnetic force, thereby filtering particles based on their velocity.

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