A velocity selector has its electric field directed...

A velocity selector has its electric field directed vertically downward, with magnitude $150 \mathrm{~N} / \mathrm{C}$. (a) Find the magnitude of the horizontal magnetic field required to select charged particles moving at $300 \mathrm{~m} / \mathrm{s}$. (b) This velocity selector is being used on protons. Compute explicitly the magnitudes of the electric and magnetic forces and show that they're equal.

Key Concepts

Lorentz Force

The Lorentz force is the combined force on a charged particle in the presence of electric and magnetic fields, described by the equation F = q(E + v × B). This equation is fundamental to understanding how charged particles behave under electromagnetic influences, as it illustrates how both the electric field and the magnetic field act on a moving charge.

Electric Field

An electric field is a vector field that represents the force per unit charge exerted on a charged object. It is central in determining the acceleration of a charged particle in space and plays a crucial role in devices like velocity selectors, where it is used to apply a known force in a specific direction.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving charged particles, with the force being perpendicular to both the velocity of the particle and the direction of the magnetic field. This property, described by the cross-product in the Lorentz force equation, is instrumental in controlling particle trajectories in many electromagnetic applications.

Velocity Selector

A velocity selector is a device that employs perpendicular electric and magnetic fields to filter particles based on their speed. It works on the principle that only particles with a speed equal to the ratio of the electric field to the magnetic field (v = E/B) will experience no net force, thereby passing through the selector without deflection.

Force Equilibrium

Force equilibrium in the context of charged particle motion occurs when the electric and magnetic forces acting on a particle balance each other exactly. This condition, crucial for the operation of a velocity selector, ensures that only particles of a specific velocity remain undeflected and continue along a predetermined path.

Transcript

Please give Ace some feedback