A charged particle moving in a magnetic field experiences a resultant force :

Options

A. In the direction perpendicular to both the field and its velocity .
B. in the direction of the field.
C. in the direction opposite to that of the field.
D. None of the above

Answer

To solve the problem of determining the direction of the resultant force experienced by a charged particle moving in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have a charged particle (let's say a positive charge, +q) moving in a magnetic field (B). The magnetic field is uniform and directed perpendicularly to the plane of motion of the charged particle.

2. **Identifying the Directions**:
- Assume the velocity (v) of the charged particle is along the positive x-axis.
- The magnetic field (B) is directed into the plane, which we can denote as the negative z-axis.

3. **Applying the Lorentz Force Law**:
- The force (F) experienced by a charged particle moving in a magnetic field is given by the Lorentz force equation:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]
- Here, \( \times \) denotes the cross product.

4. **Determining the Magnitude and Direction of the Force**:
- The magnitude of the force can be expressed as:
\[ F = qvB \sin(\theta) \]
- In our case, since the velocity (v) and the magnetic field (B) are perpendicular to each other, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1\). Therefore, the force simplifies to:
\[ F = qvB \]

5. **Using the Right-Hand Rule**:
- To find the direction of the force, we use the right-hand rule:
- Point your right thumb in the direction of the velocity (v).
- Curl your fingers in the direction of the magnetic field (B).
- Your palm will then point in the direction of the force (F).
- In this case, with v along the positive x-axis and B into the page (negative z-axis), the force will be directed upwards (positive y-axis).

6. **Conclusion**:
- The resultant force on the charged particle is perpendicular to both the velocity and the magnetic field. Therefore, the correct answer is that the force is in the direction **perpendicular to both the field and its velocity**.

### Final Answer:
The resultant force experienced by the charged particle is in the direction **perpendicular to both the magnetic field and its velocity** (Option 1).