The question is about the magnetic force on a charged particle moving in a magnetic field, given by the equation:

$\vec{F} = q\vec{v} \times \vec{B}$

Where:

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

Let’s go through each statement:

1. The magnitude of the force depends on the relative direction of $\vec{v}$ and $\vec{B}$.

   • True. The magnitude of the force is given by $|\vec{F}| = |q||\vec{v}||\vec{B}|\sin(\theta)$, where $\theta$ is the angle between $\vec{v}$ and $\vec{B}$. The force is zero if $\vec{v}$ is parallel to $\vec{B}$ (i.e., $\theta = 0^\circ$ or $180^\circ$) and maximum if they are perpendicular (i.e., $\theta = 90^\circ$).

2. The magnitude of the force is independent of the relative direction of $\vec{v}$ and $\vec{B}$.

   • False. As noted above, the force depends on the sine of the angle between $\vec{v}$ and $\vec{B}$.

3. The direction of the force will be the same direction as the magnetic field.

   • False. The magnetic force is always perpendicular to both $\vec{v}$ and $\vec{B}$, as determined by the right-hand rule for the cross product.

4. The direction of the force will be perpendicular to the magnetic field.

   • True. The force is perpendicular to both the velocity and magnetic field vectors, as determined by the cross product $\vec{v} \times \vec{B}$.

5. The magnitude of the force does not depend on whether $q$ is positive or negative.

   • False. While the magnitude of the force depends on the absolute value of $q$, the direction of the force does depend on the sign of $q$. A positive charge experiences a force in one direction, while a negative charge experiences it in the opposite direction.

Correct answers:

• The magnitude of the force depends on the relative direction of $\vec{v}$ and $\vec{B}$.
• The direction of the force will be perpendicular to the magnetic field.

Would you like further clarification or details on any of these concepts?

Related Questions:

1. What is the right-hand rule and how does it apply to magnetic forces?
2. How does the motion of a charged particle differ if it enters a magnetic field at an angle?
3. How does the magnetic force affect the speed of a charged particle?
4. How is the trajectory of a charged particle in a magnetic field determined?
5. Can a magnetic field do work on a charged particle? Why or why not?

Tip: Remember, the magnetic force on a charged particle changes its direction, not its speed, since the force is always perpendicular to its motion.