An electron falling freely under gravity entersa region of uniform horizontal magnetic field pointing north to south. The particle will be deflected towards

Options

A. east
B. west
C. north
D. south

Answer

To determine the deflection direction of an electron falling freely under gravity when it enters a uniform horizontal magnetic field pointing from North to South, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Directions:**
- The magnetic field (B) is directed from North to South. In terms of a coordinate system, we can represent this as the negative y-direction (−j cap).
- The electron is falling freely under gravity, which means it is moving in the negative z-direction (−k cap).

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

3. **Substitute the Vectors:**
- The velocity vector of the electron is \( \mathbf{v} = -k \) (since it is falling down).
- The magnetic field vector is \( \mathbf{B} = -j \) (pointing from North to South).
- Thus, we can write:
\[ \mathbf{F} = -e \left( (-k) \times (-j) \right) = -e \left( k \times j \right) \]

4. **Calculate the Cross Product:**
- Using the right-hand rule for the cross product:
\[ k \times j = i \]
- Therefore, the force becomes:
\[ \mathbf{F} = -e \cdot i \]
- Since \( e \) is positive, the force direction is \( -i \) (or in the negative x-direction).

5. **Determine the Final Direction:**
- The negative x-direction corresponds to the West.
- Since the electron has a negative charge, the force direction is opposite to what we would expect for a positive charge. Thus, the electron will be deflected towards the West.

### Conclusion:
The electron will be deflected towards the West.

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