Near the equator, the Earth's magnetic field points almost...

Near the equator, the Earth's magnetic field points almost horizontally to the north and has magnitude $B =$ 0.50 $\times$ 10$^{-4}$ T. What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?

Key Concepts

Lorentz Force

This is the force experienced by a charged particle moving through a magnetic field. It is given by the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. This concept is fundamental for understanding how magnetic fields interact with moving charges, affecting their trajectory and, in this context, counteracting gravitational force.

Gravitational Force

This is the force exerted on a mass by the Earth's gravity, calculated as F = mg, where m is the mass of the object and g is the acceleration due to gravity. It is a key concept in dynamics as it represents the weight of the object, which must be balanced by other forces in equilibrium scenarios.

Force Equilibrium

This concept refers to the state in which the sum of all forces acting on an object is zero, resulting in no net acceleration. In problems involving balancing an upward magnetic force against the downward gravitational force, force equilibrium is used to set the magnitude of the magnetic force equal to the weight, allowing for the determination of other quantities like velocity.

Vector Cross Product

This mathematical operation is used to determine the direction and magnitude of the force in the Lorentz force equation. It involves two vectors (velocity and magnetic field) and results in a third vector that is perpendicular to both, which is crucial in figuring out the correct orientation of the magnetic force to counteract gravity.

Please give Ace some feedback