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 question, let's analyze the situation step by step.

### Step 1: Understand the setup
We have a long solenoid carrying a current, which produces a magnetic field inside it. An electron is projected with a uniform velocity along the axis of this solenoid.

### Step 2: Determine the direction of the magnetic field
Inside a long solenoid, the magnetic field (\(B\)) is directed along the axis of the solenoid. 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.

### Step 3: Analyze the motion of the electron
The electron is moving along the axis of the solenoid, which means its velocity (\(v\)) is also directed along the same axis.

### Step 4: Apply the Lorentz force law
The force (\(F\)) experienced by a charged particle moving in a magnetic field is given by the Lorentz force law:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]
where \(q\) is the charge of the electron, \(\mathbf{v}\) is the velocity vector, and \(\mathbf{B}\) is the magnetic field vector.

### Step 5: Evaluate the cross product
Since the velocity of the electron is parallel to the magnetic field (both are along the axis of the solenoid), the angle between \(\mathbf{v}\) and \(\mathbf{B}\) is 0 degrees. The sine of 0 degrees is 0, which means:
\[ F = q(\mathbf{v} \times \mathbf{B}) = 0 \]
Thus, the force acting on the electron is zero.

### Step 6: Conclusion
Since there is no net force acting on the electron, it will continue to move with uniform velocity along the axis of the solenoid. Therefore, the correct answer is that the electron will continue to move with uniform velocity along the axis of the solenoid.

### Final Answer
The electron will continue to move with uniform velocity along the axis of the solenoid.

---