If an electron enters a magnetic field with its velocity pointing in the same direction as the magnetic field, then

Options

A. The electron will turn to its right
B. The electron will turn to its left
C. The velocity of the electron will increase
D. The velocity of the electron will remain unchanged

Answer

To solve the problem, we need to analyze the situation where an electron enters a magnetic field with its velocity aligned in the same direction as the magnetic field. We will use the formula for the magnetic force acting on a charged particle moving in a magnetic field.

### Step-by-step Solution:

1. **Identify the Given Information**:
- The charge of the electron is negative (−e).
- The velocity of the electron (v) is in the same direction as the magnetic field (B).

2. **Understand the Magnetic Force Formula**:
- The magnetic force (F) acting on a charged particle is given by the equation:
\[ F = q(v \times B) \]
- Here, \( q \) is the charge of the particle, \( v \) is the velocity vector, and \( B \) is the magnetic field vector.

3. **Determine the Angle Between Velocity and Magnetic Field**:
- Since the velocity of the electron is in the same direction as the magnetic field, the angle \( \theta \) between them is 0 degrees.

4. **Calculate the Cross Product**:
- The cross product \( v \times B \) can be expressed as:
\[ v \times B = vB \sin(\theta) \]
- Substituting \( \theta = 0 \):
\[ v \times B = vB \sin(0) = vB \cdot 0 = 0 \]

5. **Determine the Magnetic Force**:
- Since \( v \times B = 0 \), the magnetic force \( F \) becomes:
\[ F = -e \cdot 0 = 0 \]
- This means that there is no magnetic force acting on the electron.

6. **Conclude the Effect on the Electron's Motion**:
- With no net force acting on the electron, according to Newton's first law of motion, the electron will continue to move with its initial velocity.
- Therefore, the velocity of the electron remains unchanged.

### Final Answer:
The correct option is that the velocity of the electron will remain unchanged.

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