An electron enters an electric field with its velocity in the direction of the electric lines of force. Then

Options

A. the path of the electron will be a circle
B. the path of the electron will be a parabola
C. the velocity of the electron will decrease
D. the velocity of the electron will increase

Answer

To solve the problem of an electron entering an electric field with its velocity in the direction of the electric lines of force, we can follow these steps:

### Step 1: Understand the Electric Field and Force on the Electron
- An electric field is represented by lines of force. The direction of these lines indicates the direction of the force experienced by a positive charge.
- For an electron, which has a negative charge, the force will act in the opposite direction to the electric field.

### Step 2: Determine the Force Acting on the Electron
- The force \( \vec{F} \) acting on the electron can be calculated using the formula:
\[ \vec{F} = q \vec{E} \]
where \( q \) is the charge of the electron (which is negative) and \( \vec{E} \) is the electric field vector.
- Since the charge of the electron is negative, the force on the electron will be:
\[ \vec{F} = -e \vec{E} \]
where \( e \) is the magnitude of the charge of the electron.

### Step 3: Analyze the Motion of the Electron
- The electron is initially moving in the direction of the electric field. However, since the force acting on it is opposite to its direction of motion, the electron will experience a deceleration.
- This means that the electron's velocity will decrease over time as it moves through the electric field.

### Step 4: Determine the Path of the Electron
- Since the force is acting in the opposite direction to the velocity, the electron will not change its path to a circular or parabolic trajectory; instead, it will continue to move in a straight line but with decreasing speed.
- Therefore, the path of the electron will remain linear, but the magnitude of its velocity will decrease.

### Conclusion
- The electron will continue to move in a straight line, but its velocity will decrease over time due to the opposing force exerted by the electric field.

### Summary of the Answer
- The path of the electron will be straight, and its velocity will decrease.

---