An electron travels with speed 1.0 ×10^7 m / s between the...

An electron travels with speed $1.0 \times 10^{7} \mathrm{m} / \mathrm{s}$ between the two parallel charged plates shown in FlGURE P33.58. The plates are separated by $1.0 \mathrm{cm}$ and are charged by a $200 \mathrm{V}$ battery. What magnetic field strength and direction will allow the electron to pass between the plates without being deflected? (FIGURE CAN'T COPY)

Key Concepts

Lorentz Force

The Lorentz force is the fundamental force experienced by a charged particle moving in the presence of electric and magnetic fields. It results from the sum of the electric force (which acts in the direction of the electric field) and the magnetic force (which acts perpendicular to both the magnetic field and the particle's velocity). This concept is crucial for understanding how particles are deflected or steered in fields.

Uniform Electric Field

A uniform electric field is created, for example, between two parallel plates that are maintained at different potentials. The magnitude of the field is given by the voltage difference divided by the separation distance. This field exerts a force on any charged particle placed within it, influencing the particle's trajectory.

Uniform Magnetic Field

A uniform magnetic field exerts a force on a moving charged particle, determined by the particle's charge, its velocity, and the magnetic field strength. The direction of this force is perpendicular to both the magnetic field and the velocity, following the right-hand rule (with appropriate sign consideration for negative charges). This effect is central in applications such as particle beam steering and filtering.

Velocity Selector

A velocity selector is a device that allows only particles with a specific velocity to pass through undeflected by using crossed electric and magnetic fields. The principle is based on setting the magnitude of the electric force equal to the magnitude of the magnetic force. Only when these forces precisely balance will a particle move in a straight line, effectively selecting particles of a particular speed.

Force Equilibrium

Achieving force equilibrium involves balancing different forces acting on a particle so that there is no net acceleration in a particular direction. In the context of particles moving through crossed electric and magnetic fields, the electric force must exactly cancel the magnetic force. This equilibrium is what allows a charged particle, such as an electron, to travel in a straight line without deflection.

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