A uniform electric field and a uniform magnetic field are produced, pointed in the same direction. An electron is projected with its velocity pointing in the same direction. Then,

Options

A. the electron will turn to its right
B. the electron will turn to its left
C. the electron velocity will increase in magnitude.
D. the electron velocity will decrease in magnitude.

Answer

To solve the problem step by step, we will analyze the forces acting on the electron when it is subjected to both electric and magnetic fields that are aligned in the same direction.

### Step-by-Step Solution:

1. **Identify the Fields and Their Directions**:
- We have a uniform electric field \( \mathbf{E} \) and a uniform magnetic field \( \mathbf{B} \), both pointing in the same direction.
- An electron is projected with a velocity \( \mathbf{v} \) also in the same direction as the fields.

2. **Determine the Force Due to the Electric Field**:
- The force experienced by a charge \( Q \) in an electric field \( \mathbf{E} \) is given by:
\[ \mathbf{F_E} = Q \mathbf{E} \]
- Since the electron has a negative charge (\( Q = -e \)), the force due to the electric field will act in the opposite direction to the field:
\[ \mathbf{F_E} = -e \mathbf{E} \]

3. **Determine the Force Due to the Magnetic Field**:
- The force experienced by a charge moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) is given by:
\[ \mathbf{F_B} = Q (\mathbf{v} \times \mathbf{B}) \]
- Since both \( \mathbf{v} \) and \( \mathbf{B} \) are in the same direction, the angle \( \theta \) between them is \( 0^\circ \).
- The sine of \( 0^\circ \) is zero, thus:
\[ \mathbf{F_B} = Q \cdot v \cdot B \cdot \sin(0^\circ) = 0 \]
- Therefore, the magnetic force \( \mathbf{F_B} \) is zero.

4. **Net Force Acting on the Electron**:
- Since the magnetic force is zero, the only force acting on the electron is the electric force:
\[ \mathbf{F_{net}} = \mathbf{F_E} + \mathbf{F_B} = -e \mathbf{E} + 0 = -e \mathbf{E} \]

5. **Effect on the Electron's Motion**:
- The net force \( \mathbf{F_{net}} \) acts in the opposite direction to the velocity of the electron. This means that the electron will experience a retardation (deceleration).
- As a result, the magnitude of the electron's velocity will decrease over time.

### Conclusion:
The electron, while moving in the same direction as the electric and magnetic fields, will slow down due to the electric force acting against its motion. The magnetic force does not contribute to the motion since it is zero.