A duck accumulates a positive charge of 3.0 ×10^-8 C while flying north at speed 18 m / s . Eart

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A duck accumulates a positive charge of 3.0 ×10^-8 C while...

A duck accumulates a positive charge of 3.0 $\times 10^{-8} \mathrm{C}$ while flying north at speed 18 $\mathrm{m} / \mathrm{s}$ . Earth's magnetic field at the duck's location has a magnitude of $5.3 \times 10^{-5} \mathrm{T}$ and points in a direction $62^{\circ}$ below a horizontal line pointing north. Determine the magnitude and direction of the force exerted by Earth's magnetic field on the duck.

A duck accumulates a positive charge of 3.0 $\times 10^{-8} \mathrm{C}$ while flying north at speed 18 $\mathrm{m} / \mathrm{s}$ . Earth's magnetic field at the duck's location has a magnitude of
$5.3 \times 10^{-5} \mathrm{T}$ and points in a direction $62^{\circ}$ below a horizontal
line pointing north. Determine the magnitude and direction of the force exerted by Earth's magnetic field on the duck.

Key Concepts

Magnetic Force on a Moving Charged Particle

This concept describes how a charged particle experiences a force when moving through a magnetic field, governed by the Lorentz force law. The force is given by F = q(v × B), where q represents the charge, v the velocity vector, and B the magnetic field vector. The resulting force is always perpendicular to both the velocity of the particle and the magnetic field.

Vector Cross Product

The calculation of the magnetic force involves the vector cross product of the velocity and magnetic field vectors. This mathematical operation determines both the magnitude and the direction of the force, with the magnitude expressed as qvB sin(?), where ? is the angle between the velocity and the magnetic field.

Right-Hand Rule

The right-hand rule is a method used to determine the direction of the force vector resulting from the cross product in three-dimensional space. By orienting the fingers in the direction of the velocity and curling them towards the magnetic field, the thumb points in the direction of the magnetic force.

Decomposition of Vectors

When dealing with forces in a three-dimensional context, it is often necessary to decompose vectors into their components relative to a set of axes. This allows for a clearer analysis of the directional influence of each component, particularly when the magnetic field is not aligned with the standard coordinate directions.

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