An electron moves with a velocity of 1.0 ×107 m / s^1.0 ×10^7 m / s in the x-y plane at an ang

step 1 This problem covers the concept of the magnetic force on a moving charge. The magnetic force mag

An electron moves with a velocity of 1.0 ×107 m / s^1.0...

An electron moves with a velocity of $1.0 \times 107 \mathrm{~m} / \mathrm{s}^{1.0} \times 10^{7} \mathrm{~m} / \mathrm{s}$ in the $x-y$ plane at an angle of $45^{\circ}$ to both the $+x$ and $+y$ axes. There is a magnetic field of $3.0 \mathrm{~T}$ in the $+y$ direction. Calculate the magnetic force (magnitude and direction) on the electron. SSM Example $19-1$

Key Concepts

Right-Hand Rule

A mnemonic for determining the direction of the vector resulting from a cross product, the right-hand rule helps to predict the orientation of the magnetic force on a moving charge. By aligning the fingers according to the velocity and magnetic field vectors, the thumb indicates the force’s direction, which is essential in solving problems in electromagnetism.

Lorentz Force Concept

This principle describes the force experienced by a charged particle moving in electric and magnetic fields. In cases where only a magnetic field is present, the force is given by the cross product of the particle's velocity vector and the magnetic field vector, scaled by the particle’s charge. This fundamental concept is critical to understanding how moving charges interact with magnetic fields.

Magnetic Force on a Moving Charge

The magnetic force is specifically the part of the Lorentz force exerted on a charged particle due to its motion in a magnetic field. It is always perpendicular to both the velocity of the charge and the magnetic field, ensuring that it changes the direction of the particle's motion without doing work on it.

Vector Cross Product

This mathematical operation is used to compute the magnetic force, as it determines a vector that is perpendicular to two given vectors—in this case, the velocity of the charged particle and the magnetic field. Understanding the properties of the cross product is essential for determining both the magnitude and the direction of the resulting force.

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