A duck flying due east passes over Atlanta, where the...

A duck flying due east passes over Atlanta, where the magnetic field of the Earth is $5.0 \times 10^{-5} \mathrm{T}$ directed north. The duck has a positive charge of $4.0 \times 10^{-8} \mathrm{C}$ If the magnetic force acting on the duck is $3.0 \times 10^{-11} \mathrm{N}$ upward, what is the duck's velocity?

Key Concepts

Vector Cross Product

The magnetic component of the Lorentz force is determined by the cross product of the velocity and the magnetic field vectors. This mathematical operation results in a vector that is perpendicular to both the velocity and the magnetic field, encapsulating how the force’s direction is mutually orthogonal to these two vectors.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resultant vector produced by a cross product. In the context of the magnetic force, it helps in visualizing the direction of the force acting on a positive charge, by aligning the right-hand fingers with the velocity vector and curling them towards the magnetic field vector.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in an electromagnetic field. Its magnitude is given by F = qvB sin?, where q is the charge, v is the speed, B is the magnetic field strength, and ? is the angle between the velocity and magnetic field vectors. This law is fundamental in understanding how charged particles behave in magnetic environments.

Magnetic Field

A magnetic field represents the influence exerted by magnetic forces in a region, characterized by both a magnitude and a direction. It affects moving charged particles and other magnets, and is typically described by field lines that illustrate the direction of the force that would be experienced by a north pole.

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