A positively charged particle is moving towards the east direction and is found to get deviated towards south. What is the possible direction of the magnetic field?

Options

A. West
B. Upward
C. Downward
D. North

Answer

To determine the direction of the magnetic field when a positively charged particle is moving towards the east and deviates towards the south, we can use the right-hand rule and the relationship between force, velocity, and magnetic field.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The particle is positively charged.
- The particle is moving towards the east (let's denote this direction as the positive x-direction).
- The particle is deviating towards the south (let's denote this direction as the negative y-direction).

2. **Define the Directions:**
- Let the east direction be represented by the unit vector \( \hat{i} \) (positive x-direction).
- Let the south direction be represented by the unit vector \( -\hat{j} \) (negative y-direction).
- The magnetic field direction is what we need to find.

3. **Use the Lorentz Force Equation:**
The force \( \mathbf{F} \) on a charged particle moving in a magnetic field is given by:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
where:
- \( q \) is the charge of the particle,
- \( \mathbf{v} \) is the velocity vector,
- \( \mathbf{B} \) is the magnetic field vector.

4. **Set Up the Vectors:**
- The velocity vector \( \mathbf{v} \) can be represented as:
\[ \mathbf{v} = v \hat{i} \]
- The force vector \( \mathbf{F} \) is directed south, which can be represented as:
\[ \mathbf{F} = -F \hat{j} \]

5. **Apply the Right-Hand Rule:**
- According to the right-hand rule, to find the direction of the magnetic field \( \mathbf{B} \), we can rearrange the equation:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
- Since \( q \) is positive, the direction of \( \mathbf{F} \) is the same as \( \mathbf{v} \times \mathbf{B} \).

6. **Cross Product Analysis:**
- We know that:
\[ \mathbf{F} = -F \hat{j} \quad \text{and} \quad \mathbf{v} = v \hat{i} \]
- Therefore, we need to find \( \mathbf{B} \) such that:
\[ \hat{i} \times \mathbf{B} = -\hat{j} \]
- The cross product \( \hat{i} \times \hat{j} = \hat{k} \) (out of the plane), and to get \( -\hat{j} \), we need \( \mathbf{B} \) to be in the positive \( \hat{k} \) direction.

7. **Conclusion:**
- The direction of the magnetic field \( \mathbf{B} \) must be upwards, which can be represented as \( \hat{k} \) (positive z-direction).

### Final Answer:
The possible direction of the magnetic field is **upwards**.