https://file.aiquickdraw.com/mathbot/file/1728257109847yl5i0v2z.jpg

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.

Which of the following are true about the magnetic force of a charge q, moving with velocity v in a magnetic field B?

This problem explores the magnetic force on a charged particle moving in a magnetic field, using the formula F = q(v × B). It covers the dependence of force magnitude on the angle between velocity and the magnetic field, and the right-hand rule for force direction.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation