In a certain region of space, there is a uniform electric field 𝐄=3.0 ×10^4 V / m directed due e

step 1 All right, so we've got an electron, which is going through a magnetic and an electric field, wh

In a certain region of space, there is a uniform electric...

In a certain region of space, there is a uniform electric field $\overrightarrow{\mathbf{E}}=3.0 \times 10^{4} \mathrm{V} / \mathrm{m}$ directed due east and a uniform magnetic field $\overrightarrow{\mathbf{B}}=0.080 \mathrm{T}$ also directed due east. What is the electromagnetic force on an electron moving due south at $5.0 \times 10^{6} \mathrm{m} / \mathrm{s} ?$

In a certain region of space, there is a uniform electric field $\overrightarrow{\mathbf{E}}=3.0 \times 10^{4} \mathrm{V} / \mathrm{m}$ directed due east and a uniform magnetic field $\overrightarrow{\mathbf{B}}=0.080 \mathrm{T}$ also directed due
east. What is the electromagnetic force on an electron moving due south at $5.0 \times 10^{6} \mathrm{m} / \mathrm{s} ?$

Key Concepts

Lorentz Force Law

The Lorentz force law is a cornerstone in electromagnetism that describes the total force experienced by a charged particle moving in electric and magnetic fields. It tells us that the force is given by F = q(E + v × B), where E is the electric field, v is the velocity of the particle, B is the magnetic field, and q is the charge. This principle is fundamental when analyzing the dynamics of charges in various fields and underpins many electromagnetic devices and phenomena.

Electric Force

The electric force on a charged particle is produced by the presence of an electric field and is given by F = qE. This force acts in the direction of the electric field for a positive charge and in the opposite direction for a negative charge. It is a direct, scalar multiplication of the charge and the electric field, and is independent of the particle’s motion.

Magnetic Force

The magnetic force comes into play when a charged particle is in motion through a magnetic field. It is determined by the cross product F = q(v × B), meaning that its magnitude and direction depend on both the speed and direction of the particle's velocity as well as the magnetic field. This force is always perpendicular to both the velocity and the magnetic field, which can lead to curved trajectories of the moving charge.

Vector Cross Product

The vector cross product is a mathematical operation used to determine the direction and magnitude of the magnetic force on a moving charge. When calculating v × B, the resulting vector is perpendicular to the plane containing v and B, with its direction given by the right-hand rule. This operation is central to understanding how the magnetic component of the Lorentz force acts in three-dimensional space.

Charge Sign and Force Direction

The sign of the charge plays a crucial role in determining the direction of both the electric and magnetic forces. For instance, a negative charge like that of an electron will experience forces in the opposite direction to those predicted for a positive charge when subjected to both electric fields and the cross product in magnetic fields. This reversal is essential for accurately determining the net force on a charged particle in an electromagnetic environment.

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