A 0.75 -T magnetic field points west. Find the magnitude and...

A 0.75 -T magnetic field points west. Find the magnitude and direction of the force on a $+2.5-\mu \mathrm{C}$ charge moving southward at $5.5 \mathrm{~m} / \mathrm{s} .$ (a) $1.0 \times 10^{-5} \mathrm{~N}$, straight up; (b) $1.0 \times 10^{-5} \mathrm{~N}$, straight down; (c) $1.0 \times 10^{-2} \mathrm{~N},$ straight up; (d) $1.0 \times 10^{-2} \mathrm{~N},$ straight down.

Key Concepts

Magnetic Force on a Moving Charge

This concept is based on the Lorentz force law, which states that a charged particle moving in a magnetic field experiences a force given by F = q(v × B). The direction of the force is perpendicular to both the velocity of the charge and the magnetic field, and its magnitude is proportional to the charge, its speed, and the strength of the magnetic field.

Cross Product

The cross product is an operation in vector algebra that yields a vector perpendicular to two given vectors. In physics, it is used to calculate the magnetic force on a moving charge, as the force’s magnitude and its perpendicular direction relative to the velocity and the magnetic field are determined by this operation.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the vector obtained from a cross product. It is applied by orienting the right hand so that the fingers point in the direction of the first vector (velocity) and then curling them towards the second vector (magnetic field), with the thumb then pointing in the direction of the resultant magnetic force for a positive charge.

Unit Conversion

Unit conversion is essential in problems involving physical quantities to ensure that all values are in the correct units for analysis. For example, converting microcoulombs to coulombs is crucial when calculating forces in SI units, ensuring the accuracy and consistency of the results.

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