A velocity selector having uniform perpendicular electric...

A velocity selector having uniform perpendicular electric and magnetic fields is shown in Figure 20.57 . The electric field is provided by a $150 \mathrm{~V}$ de battery connected across two large parallel metal plates that are $4.50 \mathrm{~cm}$ apart. (a) What must be the magnitude of the magnetic field so that charges having a velocity of $3.25 \mathrm{~km} / \mathrm{s}$ perpendicular to the fields will pass through undeflected? (b) Show how the magnetic field should point in the region between the plates.

Key Concepts

Uniform Magnetic Field

A uniform magnetic field is one where both the magnitude and the direction remain constant throughout the considered area. In the context of a velocity selector, such a field is critical because it provides a consistent magnetic force on moving charges, which must counterbalance the electric force for particles moving at the designated velocity.

Velocity Selector

A velocity selector is a device that uses perpendicular electric and magnetic fields to allow only charged particles with a specific velocity to pass through undeflected. This works by ensuring that the electric force acting on the particle is exactly balanced by the magnetic force, so that the net force is zero for particles moving at the selected speed.

Lorentz Force

The Lorentz force is the sum of the electric and magnetic forces acting on a charged particle. It is given by the equation F = q(E + v × B), where q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. This principle underlies the operation of devices that control or measure the motion of charged particles.

Uniform Electric Field

A uniform electric field is one in which the electric force experienced by a charged particle is constant in magnitude and direction throughout the region. In a velocity selector, a constant potential difference across parallel plates creates such a field, ensuring that every charged particle experiences the same electric force.

Right-Hand Rule

The right-hand rule is a tool used to determine the direction of the magnetic force on a moving positive charge within a magnetic field. This rule is vital in settings such as a velocity selector, where understanding and controlling the direction of forces allows for the precise manipulation of charged particle trajectories.

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