A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B.The path of the charge particle will be

Options

A. straight along the direction of magnetic field `B`
B. helical path with the axis along magnetic field `B`
C. helical path with the axis perpendicular to the direction of magnetic field `B`
D. circular path

Answer

To solve the problem of a charged particle moving in a magnetic field with components of velocity both along and perpendicular to the magnetic field, we can analyze the motion step by step.

### Step-by-Step Solution:

1. **Understanding the Motion in a Magnetic Field**:
- A charged particle moving in a magnetic field experiences a magnetic force given by the Lorentz force equation:
\[ \vec{F} = q(\vec{v} \times \vec{B}) \]
- Here, \(q\) is the charge of the particle, \(\vec{v}\) is the velocity of the particle, and \(\vec{B}\) is the magnetic field.

2. **Components of Velocity**:
- The velocity of the charged particle can be broken down into two components:
- \(v_{\parallel}\): the component of velocity parallel to the magnetic field \(B\).
- \(v_{\perpendicular}\): the component of velocity perpendicular to the magnetic field \(B\).

3. **Effect of the Magnetic Field**:
- The component of velocity parallel to the magnetic field (\(v_{\parallel}\)) does not experience any magnetic force. Therefore, it continues to move in a straight line along the direction of the magnetic field.
- The component of velocity perpendicular to the magnetic field (\(v_{\perpendicular}\)) will experience a magnetic force, causing the particle to undergo circular motion in the plane perpendicular to the magnetic field.

4. **Resulting Path of the Charged Particle**:
- The combination of linear motion along the magnetic field (due to \(v_{\parallel}\)) and circular motion in the plane perpendicular to the magnetic field (due to \(v_{\perpendicular}\)) results in a helical path.
- The particle moves in a helical trajectory around the magnetic field lines.

5. **Conclusion**:
- Therefore, the path of the charged particle will be helical, with the axis of the helix aligned along the direction of the magnetic field \(B\).

### Final Answer:
The path of the charged particle will be helical along the axis of the magnetic field \(B\).