An electron is travelling horizontally towards east. A magnetic field in vertically downward direction exerts a force on the electron along

Options

A. East
B. West
C. North
D. South

Explanation

To solve the problem of determining the direction of the force exerted on an electron traveling east in a vertically downward magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The electron is moving horizontally towards the east.
- The magnetic field is directed vertically downwards.

2. **Determine the Charge of the Electron**:
- The charge of an electron is negative (Q = -e).

3. **Use the Formula for Magnetic Force**:
- The magnetic force (F) on a charged particle moving in a magnetic field is given by the equation:
\[ F = Q(\mathbf{v} \times \mathbf{B}) \]
- Here, \( \mathbf{v} \) is the velocity vector of the electron and \( \mathbf{B} \) is the magnetic field vector.

4. **Define the Vectors**:
- Let the velocity vector \( \mathbf{v} \) point towards the east (right).
- Let the magnetic field vector \( \mathbf{B} \) point downwards (into the paper).

5. **Apply the Right-Hand Rule (Fleming's Left-Hand Rule)**:
- According to Fleming's Left-Hand Rule, to find the direction of the force:
- Point your **middle finger** in the direction of the velocity (east).
- Point your **index finger** in the direction of the magnetic field (downwards).
- Your **thumb** will then point in the direction of the force on a positive charge.

6. **Determine the Direction of the Force**:
- Following the right-hand rule, if we consider the electron as a positive charge, the thumb points upwards (north).
- However, since the electron has a negative charge, the actual force will be in the opposite direction of the thumb, which means the force will point downwards (south).

7. **Conclusion**:
- Therefore, the force exerted on the electron is directed towards the south.

### Final Answer:
The force on the electron is directed **south**.

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