To determine the direction of the magnetic force on the electron, we use the right-hand rule for the force experienced by a charged particle moving in a magnetic field. The force on a charged particle (such as an electron) is given by:

$\vec{F} = q (\vec{v} \times \vec{B}),$

where:

• $\vec{F}$ is the force,
• $q$ is the charge of the particle,
• $\vec{v}$ is the velocity vector, and
• $\vec{B}$ is the magnetic field vector.

Given:

• The electron moves in the negative $x$-direction ($\vec{v}$ is in the $-\hat{i}$ direction).
• The magnetic field is in the negative $y$-direction ($\vec{B}$ is in the $-\hat{j}$ direction).

Steps:

1. Use the right-hand rule for the cross product $\vec{v} \times \vec{B}$. Point your fingers in the direction of $\vec{v}$ (negative $x$) and curl them towards $\vec{B}$ (negative $y$). Your thumb will point in the positive $z$-direction.

2. Since the electron is negatively charged, the force direction will be opposite to the direction given by the right-hand rule. Therefore, the magnetic force will be in the negative $z$-direction.

Answer:

The magnetic force on the electron is in the negative $z$-direction.

Would you like further details or have any questions about this explanation?

Here are five additional related questions to expand your understanding:

1. What would happen to the direction of the magnetic force if the particle were positively charged instead of negatively charged?
2. How does the magnitude of the magnetic force change if the speed of the electron is doubled?
3. What is the direction of the magnetic force if the magnetic field is oriented in the positive $y$-direction while the electron still moves in the negative $x$-direction?
4. How would the motion of the electron change if the magnetic field had a component in the $z$-direction as well?
5. How does the magnetic force affect the velocity of a charged particle? Does it change the speed or the direction?

Tip: Remember that the magnetic force is always perpendicular to both the velocity of the charged particle and the magnetic field, which results in circular or helical motion for the particle.