A moving electron enters a uniform and perpendicular magnetic field. Inside the magnetic field, the electron travels along :

Options

A. a straight line
B. a parabola
C. a circle
D. a hyperbola

Answer

To solve the problem of a moving electron entering a uniform and perpendicular magnetic field, we can follow these steps:

### Step 1: Understand the Motion of the Electron
When a charged particle, such as an electron, enters a magnetic field, it experiences a magnetic force. The direction of this force is given by the right-hand rule and is always perpendicular to both the velocity of the electron and the magnetic field.

**Hint:** Remember that the magnetic force acts perpendicular to the velocity of the charged particle.

### Step 2: Apply the Lorentz Force Equation
The magnetic force \( F \) acting on the electron can be expressed using the Lorentz force equation:
\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]
where:
- \( q \) is the charge of the electron,
- \( v \) is the velocity of the electron,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity and the magnetic field direction.

Since the magnetic field is perpendicular to the motion of the electron, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1 \). Thus, the equation simplifies to:
\[ F = q \cdot v \cdot B \]

**Hint:** The force is maximized when the magnetic field is perpendicular to the motion of the charged particle.

### Step 3: Analyze the Direction of the Force
The magnetic force acts as a centripetal force that changes the direction of the electron's velocity without changing its speed. This means that the electron will not move in a straight line but will instead follow a curved path.

**Hint:** Consider how the direction of the force changes as the electron moves through the magnetic field.

### Step 4: Determine the Path of the Electron
Since the force is always perpendicular to the velocity, the electron will move in a circular path. The radius of this circular motion can be determined using the centripetal force equation, but for this question, we only need to identify the type of path.

**Hint:** Recall that uniform circular motion occurs when a constant force acts perpendicular to the direction of motion.

### Conclusion
Therefore, the correct answer is that the electron travels along a circular path when it enters a uniform and perpendicular magnetic field.

**Final Answer:** The electron travels along a **circle** (Option C).