An electron is projected along the axis of a current carrying solenoid of length I, with uniform velocity then:

Options

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

Explanation

To solve the problem, we will analyze the motion of an electron projected along the axis of a current-carrying solenoid.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a solenoid carrying a current, which generates a magnetic field inside it. The length of the solenoid is given as \( l \).
- An electron is projected along the axis of the solenoid with a uniform velocity \( v \).

2. **Direction of Magnetic Field**:
- The magnetic field \( \vec{B} \) inside a long solenoid is directed along its axis (the same direction as the current). According to the right-hand rule, if you curl the fingers of your right hand in the direction of the current, your thumb points in the direction of the magnetic field.

3. **Velocity of the Electron**:
- The electron is moving along the same axis as the magnetic field, which means the velocity \( \vec{V} \) of the electron is parallel to the magnetic field \( \vec{B} \).

4. **Magnetic Force on the Electron**:
- The magnetic force \( \vec{F}_m \) acting on a charged particle moving in a magnetic field is given by the equation:
\[ \vec{F}_m = q (\vec{V} \times \vec{B}) \]
- Here, \( q \) is the charge of the electron (which is negative), \( \vec{V} \) is the velocity vector of the electron, and \( \vec{B} \) is the magnetic field vector.

5. **Cross Product**:
- Since the velocity \( \vec{V} \) and the magnetic field \( \vec{B} \) are parallel, the cross product \( \vec{V} \times \vec{B} \) will be zero:
\[ \vec{V} \times \vec{B} = 0 \]
- Therefore, the magnetic force \( \vec{F}_m \) acting on the electron is also zero:
\[ \vec{F}_m = q \cdot 0 = 0 \]

6. **Conclusion**:
- Since there is no magnetic force acting on the electron, it will not experience any acceleration or change in velocity. Thus, the electron will continue to move with its initial uniform velocity \( v \) along the axis of the solenoid.

### Final Answer:
The electron will continue to move with uniform velocity.