The condition under which a point charge moving through a magnetic field, experiences maximum force (in terms of magntiude) is

Options

A. `vecv||vecB`
B. `theta=45^(@)` between v and B
C. `vecv_|_vecB`
D. charge is positive

Answer

To solve the problem of determining the condition under which a point charge moving through a magnetic field experiences maximum force, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lorentz Force**: The force \( F \) experienced by a point charge \( q \) moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) is given by the Lorentz force equation:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]

2. **Magnitude of the Force**: The magnitude of this force can be expressed as:
\[ F = qvB \sin \theta \]
where:
- \( F \) is the magnitude of the force,
- \( q \) is the charge,
- \( v \) is the speed of the charge,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \).

3. **Identify Constants**: In this scenario, \( q \), \( v \), and \( B \) are constants. Therefore, the force \( F \) depends on the term \( \sin \theta \).

4. **Maximize the Sine Function**: The sine function reaches its maximum value of 1 when:
\[ \sin \theta = 1 \]
This occurs when:
\[ \theta = 90^\circ \quad \text{or} \quad \theta = \frac{\pi}{2} \text{ radians} \]

5. **Conclusion**: For the force \( F \) to be maximized, the angle \( \theta \) between the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \) must be \( 90^\circ \). This means that the velocity vector \( \mathbf{v} \) must be perpendicular to the magnetic field vector \( \mathbf{B} \).

### Final Answer:
The condition under which a point charge moving through a magnetic field experiences maximum force is when \( \mathbf{v} \) is perpendicular to \( \mathbf{B} \).