A velocity selector having uniform perpendicular electric...

A velocity selector having uniform perpendicular electric and magnetic fields is shown in Figure $20.59 .$ The electric field is provided by a 150 $\mathrm{V} \mathrm{DC}$ 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

Velocity Selector

A velocity selector is a device that utilizes perpendicular electric and magnetic fields to filter and allow only those charged particles with a specific velocity to pass through undeflected. This occurs because the electric force on a charge is balanced by the magnetic force for particles at that particular speed, ensuring that only particles with the correct velocity will have their forces cancel out completely.

Electric Field

An electric field is a region of space where charged particles experience a force proportional to their charge. In devices like velocity selectors, a uniform electric field is often created by placing two plates at different electric potentials, and the field strength is determined by the potential difference divided by the distance between the plates.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving charged particles perpendicular to both the particle’s velocity and the magnetic field direction. In the context of velocity selectors, the magnetic field is arranged such that its force on the particle cancels the electric force when the particle’s velocity is at the specific value needed, allowing only particles with that velocity to pass through undeflected.

Lorentz Force

The Lorentz force is the total force exerted on a charged particle moving in electric and magnetic fields. It is given by the sum of the electric force (charge times electric field) and the magnetic force (charge times velocity cross magnetic field). In velocity selectors, the condition for no deflection is achieved when these two forces are equal in magnitude and opposite in direction.

Transcript

Please give Ace some feedback