An electron enters a region of space in which there exists an electric field 'E' and magnetic field 'B'. If the electron continues to move in the same direction with same velocity as before, the NOT possible case among the following is

Options

A. E = 0 & B=0
B. `Ene0&Bne0`
C. `Ene0&B=0`
D. `E=0&Bne0`

Answer

To solve the problem, we need to analyze the conditions under which an electron can continue to move in the same direction with the same velocity when it enters a region with electric and magnetic fields.

### Step-by-Step Solution:

1. **Understanding the Forces Acting on the Electron:**
The motion of the electron is influenced by the Lorentz force, which is given by the equation:
\[ \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the electron, \( \mathbf{E} \) is the electric field, \( \mathbf{B} \) is the magnetic field, and \( \mathbf{v} \) is the velocity of the electron.

2. **Case Analysis:**
We need to analyze the four given cases to determine which one is not possible when the electron continues to move with the same velocity.

- **Case 1:** \( \mathbf{E} = 0 \) and \( \mathbf{B} = 0 \)
- In this case, there are no forces acting on the electron, so it can continue moving with the same velocity. **This case is possible.**

- **Case 2:** \( \mathbf{E} \neq 0 \) and \( \mathbf{B} \neq 0 \)
- Here, the electron can experience forces from both fields. If we set \( \mathbf{E} = -\mathbf{v} \times \mathbf{B} \), the net force becomes zero, allowing the electron to maintain its velocity. **This case is also possible.**

- **Case 3:** \( \mathbf{E} \neq 0 \) and \( \mathbf{B} = 0 \)
- In this scenario, the presence of an electric field means that the electron will experience a force \( \mathbf{F} = q\mathbf{E} \), which will cause it to accelerate. Therefore, it cannot maintain the same velocity. **This case is not possible.**

- **Case 4:** \( \mathbf{E} = 0 \) and \( \mathbf{B} \neq 0 \)
- In this case, the electron will experience a magnetic force given by \( \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \). If the velocity \( \mathbf{v} \) is parallel or anti-parallel to \( \mathbf{B} \), the force will be zero, allowing the electron to maintain its velocity. **This case is possible.**

3. **Conclusion:**
Based on the analysis, the case where \( \mathbf{E} \neq 0 \) and \( \mathbf{B} = 0 \) is the only scenario where the electron cannot continue moving with the same velocity. Therefore, the answer is:
\[ \text{Not possible case: } \mathbf{E} \neq 0 \text{ and } \mathbf{B} = 0 \]