The magnitude of magnetic force is expressed as?

Options

A. `F _(m) = q v B sin theta`
B. ` F_(m) = q v B cos theta `
C. `F_(m) = q v B tan theta `
D. `F _(m) = qv B // sin theta `

Explanation

To find the magnitude of the magnetic force, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Magnetic Force**: The magnetic force (\( F_m \)) experienced by a charged particle moving in a magnetic field is given by the equation involving the charge (\( q \)), the velocity (\( v \)), and the magnetic field (\( B \)).

2. **Using the Cross Product**: The magnetic force can be expressed using the vector cross product:
\[ \mathbf{F_m} = q (\mathbf{v} \times \mathbf{B}) \]
Here, \( \mathbf{v} \) is the velocity vector of the charged particle, and \( \mathbf{B} \) is the magnetic field vector.

3. **Magnitude of the Cross Product**: The magnitude of the cross product \( \mathbf{v} \times \mathbf{B} \) is given by:
\[ |\mathbf{v} \times \mathbf{B}| = |\mathbf{v}| |\mathbf{B}| \sin \theta \]
where \( \theta \) is the angle between the velocity vector and the magnetic field vector.

4. **Substituting into the Force Equation**: Now, substituting the magnitude of the cross product back into the force equation gives:
\[ |\mathbf{F_m}| = q |\mathbf{v}| |\mathbf{B}| \sin \theta \]

5. **Final Expression**: Thus, the magnitude of the magnetic force can be expressed as:
\[ F_m = q v B \sin \theta \]

6. **Identifying the Correct Option**: From the options given in the question, the correct expression for the magnitude of the magnetic force is:
\[ F_m = q v B \sin \theta \]
which corresponds to option number one.

### Conclusion:
The magnitude of the magnetic force is expressed as:
\[ F_m = q v B \sin \theta \]