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 abou the axis.
C. the electronw ill experience a force at `45^(@)` to the xis 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 question, we need to analyze the motion of an electron projected along the axis of a long current-carrying solenoid. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a long solenoid carrying a current. The magnetic field inside a long solenoid is uniform and directed along the axis of the solenoid.
- An electron is projected with uniform velocity along the same axis.

2. **Direction of Magnetic Field**:
- According to the right-hand thumb rule, if the current in the solenoid is flowing in a certain direction, the magnetic field inside the solenoid will also be directed along the axis of the solenoid.

3. **Velocity and Magnetic Field**:
- The electron is moving along the axis of the solenoid, which means its velocity vector (V) is parallel to the magnetic field vector (B).

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

5. **Calculating the Force**:
- Since the velocity and magnetic field are parallel (angle between them is 0 degrees), the cross product \(\mathbf{V} \times \mathbf{B}\) becomes zero:
\[ F = Q(\mathbf{V} \times \mathbf{B}) = QV B \sin(0) = 0 \]
- Therefore, the net force acting on the electron is zero.

6. **Conclusion about Motion**:
- Since the net force is zero, according to Newton's first law of motion, the electron will continue to move with uniform velocity along the axis of the solenoid. There will be no acceleration or change in speed.

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