A uniform magnetic field `B` and a uniform electric field `E` act in a common region. An electron is entering this region of space. The correct arrangement for it to escape undeviated is

Options

A.
B.
C.
D.

Explanation

To determine the correct arrangement for an electron to escape undeviated in the presence of uniform electric and magnetic fields, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Acting on the Electron**:
- The force due to the electric field \( E \) acting on the electron is given by:
\[ F_E = Q \cdot E \]
- The force due to the magnetic field \( B \) acting on the electron when it is moving with velocity \( v \) is given by:
\[ F_B = Q \cdot (v \times B) \]
- Here, \( Q \) is the charge of the electron (which is negative).

2. **Condition for Undeviated Motion**:
- For the electron to move undeviated, the net force acting on it must be zero. This means that the electric force must be equal in magnitude and opposite in direction to the magnetic force:
\[ F_E + F_B = 0 \quad \Rightarrow \quad F_E = -F_B \]

3. **Direction of Forces**:
- The electric force \( F_E \) acts in the direction of the electric field \( E \).
- The magnetic force \( F_B \) acts in the direction given by the right-hand rule (for a positive charge), but since we are dealing with an electron (negative charge), the direction of \( F_B \) will be opposite to that predicted by the right-hand rule.

4. **Analyzing Each Arrangement**:
- **Option A**: If \( E \) is in one direction and \( B \) is perpendicular to it, the forces will not cancel. Hence, this option is not valid.
- **Option B**: Similar analysis shows that the forces will not balance. Hence, this option is not valid.
- **Option C**: If the electric field \( E \) is in one direction and the magnetic field \( B \) is perpendicular to it, the forces can balance if they are in opposite directions. This option is valid.
- **Option D**: The forces will not cancel out as they are not in opposite directions. Hence, this option is not valid.

5. **Conclusion**:
- The only arrangement that allows the electron to escape undeviated is **Option C**.

### Final Answer:
The correct arrangement for the electron to escape undeviated is **Option C**.