An electron enters a region where magnetic field (B) and electric field (E ) are mutually perpendicular, then

Options

A. it will always move in the direction of B
B. it will always move in the direction of E
C. it always possess circular motion
D. it can go undeflected also

Answer

To solve the problem, we need to analyze the motion of an electron in a region where the magnetic field (B) and electric field (E) are mutually perpendicular. We will determine under what conditions the electron can move undeflected.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- When a charged particle (like an electron) moves in an electric field (E) and a magnetic field (B), it experiences forces due to both fields.
- The force due to the electric field (F_E) is given by:
\[ F_E = qE \]
where \( q \) is the charge of the electron (which is negative) and \( E \) is the electric field strength.

2. **Magnetic Force**:
- The force due to the magnetic field (F_B) on a moving charge is given by:
\[ F_B = q(\mathbf{v} \times \mathbf{B}) \]
where \( \mathbf{v} \) is the velocity of the electron and \( \mathbf{B} \) is the magnetic field.

3. **Condition for Undeflected Motion**:
- For the electron to move undeflected, the net force acting on it must be zero. This means that the electric force must equal the magnetic force in magnitude but opposite in direction:
\[ F_E + F_B = 0 \implies F_E = -F_B \]
- Therefore, we can write:
\[ qE = q(\mathbf{v} \times \mathbf{B}) \]
- Since \( q \) is the same for both forces, we can cancel \( q \) (noting that \( q \) is negative for an electron):
\[ E = vB \]

4. **Direction of Fields and Velocity**:
- For the forces to balance, the velocity vector (\( \mathbf{v} \)) must be perpendicular to both the electric field (\( \mathbf{E} \)) and the magnetic field (\( \mathbf{B} \)).
- If \( \mathbf{E} \) is in the negative z-direction and \( \mathbf{B} \) is in the positive y-direction, then the velocity must be in the positive x-direction (or any direction that maintains the perpendicularity).

5. **Conclusion**:
- If the conditions are met (i.e., \( E = vB \) and all vectors are mutually perpendicular), the electron can move undeflected through the region where both fields exist.

### Final Answer:
The electron can go undeflected if the electric and magnetic forces balance each other.