An ionized gas contains both positive and negative ions . If it is subjected simultaneously to an electric field along the ` +x` - direction and a magnetic field along the ` +y` - direction and the negative ions towardws `-y` - direction

Options

A. positive ions deflect towards +y- direction and negative ions-y-direction
B. all ions deflect towards +y-direction
C. all ions deflect towards -y-direction
D. positive ions deflect towards -z-direction and negative ions towards -z
-direction

Answer

To solve the problem, we need to analyze the forces acting on both positive and negative ions in an ionized gas when subjected to an electric field and a magnetic field.

### Step-by-Step Solution:

1. **Identify the Directions of the Fields**:
- The electric field \( \vec{E} \) is directed along the \( +x \) direction.
- The magnetic field \( \vec{B} \) is directed along the \( +y \) direction.

2. **Determine the Force on Positive Ions**:
- The force \( \vec{F} \) on a charged particle in an electric field is given by \( \vec{F} = q \vec{E} \).
- For positive ions (charge \( q > 0 \)):
\[ \vec{F}_{E, +} = q \vec{E} \quad \text{(in the direction of } \vec{E} \text{)} \]
- Since \( \vec{E} \) is in the \( +x \) direction, the force on positive ions will also be in the \( +x \) direction.

3. **Determine the Force on Negative Ions**:
- For negative ions (charge \( q < 0 \)):
\[ \vec{F}_{E, -} = q \vec{E} \quad \text{(in the opposite direction of } \vec{E} \text{)} \]
- Therefore, the force on negative ions will be in the \( -x \) direction.

4. **Determine the Magnetic Force**:
- The magnetic force on a charged particle moving in a magnetic field is given by \( \vec{F}_{B} = q (\vec{v} \times \vec{B}) \).
- The velocity \( \vec{v} \) of the ions is assumed to be in the \( +x \) direction (for both positive and negative ions).
- The magnetic field \( \vec{B} \) is in the \( +y \) direction.

5. **Calculate the Magnetic Force for Positive Ions**:
- For positive ions:
\[ \vec{F}_{B, +} = q (\vec{v} \times \vec{B}) = q (v \hat{i} \times B \hat{j}) = qvB \hat{k} \]
- This force acts in the \( +z \) direction (out of the plane).

6. **Calculate the Magnetic Force for Negative Ions**:
- For negative ions:
\[ \vec{F}_{B, -} = q (\vec{v} \times \vec{B}) = q (v \hat{i} \times B \hat{j}) = -qvB \hat{k} \]
- This force acts in the \( -z \) direction (into the plane).

7. **Combine the Forces**:
- For positive ions, the electric force acts in the \( +x \) direction and the magnetic force acts in the \( +z \) direction.
- For negative ions, the electric force acts in the \( -x \) direction and the magnetic force acts in the \( -z \) direction.

8. **Conclusion**:
- The net effect is that positive ions will move in the \( +x \) direction and experience an upward force in the \( +z \) direction, while negative ions will move in the \( -x \) direction and experience a downward force in the \( -z \) direction.
- Thus, the negative ions will deflect towards the \( -y \) direction due to the electric and magnetic forces acting on them.

### Final Answer:
The negative ions will deflect towards the \( -y \) direction.