An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?

Options

A. The electron will be accelerated along the axis.
B. The electron path will be circular about the axis.
C. The electron will experience a force at `45^@` to the axis and hence execute a helical path.
D. The electron will continue to move with uniform velocity along the axis of the solenoid.

Explanation

To solve the problem, we need to analyze the motion of an electron projected with uniform velocity along the axis of a current-carrying solenoid.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a long solenoid carrying a current. This current generates a magnetic field inside the solenoid. The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.

2. **Direction of the Magnetic Field**:
- Using the right-hand rule, if the current flows in a certain direction (let's say clockwise when viewed from one end), the magnetic field lines inside the solenoid will point in the direction of the solenoid's axis.

3. **Electron's Motion**:
- The electron is projected with a uniform velocity along the axis of the solenoid. This means that the velocity vector of the electron is aligned with the magnetic field vector.

4. **Applying the Lorentz Force Law**:
- The force acting on a charged particle moving in a magnetic field is given by the Lorentz force equation:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the electron, \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector.

5. **Calculating the Force**:
- Since the electron's velocity \( \mathbf{v} \) is parallel to the magnetic field \( \mathbf{B} \), the angle \( \theta \) between them is 0 degrees.
- The sine of 0 degrees is 0:
\[ F = qvB \sin(0) = 0 \]
- Therefore, the magnetic force acting on the electron is zero.

6. **Conclusion**:
- Since there is no magnetic force acting on the electron, it will not experience any acceleration. The electron will continue to move with its initial uniform velocity along the axis of the solenoid.

7. **Final Answer**:
- The correct statement is: "The electron will continue to move in uniform velocity along the axis of the solenoid."