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 unchahged

Answer

To solve the problem, we need to analyze the situation where an electron enters a magnetic field with its velocity pointing in the same direction as the magnetic field.

### Step-by-Step Solution:

1. **Identify the Direction of Velocity and Magnetic Field:**
- The electron is moving with a velocity \( \vec{V} \) and enters a magnetic field \( \vec{B} \). According to the problem, both \( \vec{V} \) and \( \vec{B} \) are in the same direction.

2. **Use the Lorentz Force Formula:**
- The force \( \vec{F} \) experienced by a charged particle in a magnetic field is given by the Lorentz force equation:
\[ \vec{F} = -e (\vec{V} \times \vec{B}) \]
- Here, \( e \) is the charge of the electron (which is negative).

3. **Calculate the Cross Product:**
- The cross product \( \vec{V} \times \vec{B} \) gives the magnitude of the force based on the angle \( \theta \) between the velocity and magnetic field vectors:
\[ |\vec{F}| = -e |\vec{V}| |\vec{B}| \sin(\theta) \]
- Since \( \vec{V} \) and \( \vec{B} \) are parallel, the angle \( \theta \) between them is \( 0^\circ \).

4. **Evaluate the Sine of the Angle:**
- The sine of \( 0^\circ \) is:
\[ \sin(0^\circ) = 0 \]
- Therefore, the force becomes:
\[ |\vec{F}| = -e |\vec{V}| |\vec{B}| \cdot 0 = 0 \]

5. **Conclusion about the Motion of the Electron:**
- Since the force \( \vec{F} \) is zero, the electron does not experience any acceleration. According to Newton's first law of motion, if no net force acts on an object, it will continue to move at a constant velocity.
- Thus, the electron will continue to move with the same velocity \( \vec{V} \) in the direction of the magnetic field.

### Final Answer:
The electron will continue to move with a constant velocity in the same direction as the magnetic field.

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