An electron that has an instantaneous velocity of v⃗=(-5.0 ×10^6 m / s) î+(3.0 ×10^6 m / s) ĵ

step 1 In this problem on the topic of magnetic fields, we are told that at an instant an electron has

An electron that has an instantaneous velocity of v⃗=(-5.0...

An electron that has an instantaneous velocity of $$ \vec{v}=\left(-5.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\right) \hat{\mathrm{i}}+\left(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\right) \hat{\mathrm{j}} $$ is moving through the uniform magnetic field $\vec{B}=(0.030 \mathrm{~T}) \hat{\mathrm{i}}-$ $(0.15 \mathrm{~T}) \hat{j}$. (a) Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.

An electron that has an instantaneous velocity of
$$
\vec{v}=\left(-5.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\right) \hat{\mathrm{i}}+\left(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\right) \hat{\mathrm{j}}
$$
is moving through the uniform magnetic field $\vec{B}=(0.030 \mathrm{~T}) \hat{\mathrm{i}}-$ $(0.15 \mathrm{~T}) \hat{j}$. (a) Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.

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Key Concepts

Particle Charge and Its Sign

The sign and magnitude of a particle's charge play a crucial role in determining the direction as well as the magnitude of the magnetic force. For example, electrons and protons have charges of opposite signs, which results in the force acting in opposite directions for the same velocity and magnetic field conditions.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field, given by the equation F = q (v × B). This concept is fundamental in electromagnetism and determines how charged particles are influenced by magnetic fields based on their velocity and the field's orientation.

Vector Cross Product

The vector cross product is a mathematical operation used to determine a vector that is perpendicular to two given vectors. In the context of the Lorentz force, it provides both the magnitude and direction of the force on a charged particle, relying on the sine of the angle between the velocity and magnetic field vectors.

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