If the direction of the initial velocity of a charged particle is neither along nor perpendicular to that of the magnetic field, then the orbit will be

Options

A. a straight line
B. an ellipse
C. a circle
D. a helix

Answer

To determine the path of a charged particle moving in a magnetic field when its initial velocity is neither along nor perpendicular to the magnetic field, we can analyze the forces acting on the particle and the resulting motion.

### Step-by-Step Solution:

1. **Understanding the Motion of Charged Particles in Magnetic Fields:**
When a charged particle moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ \vec{F} = q(\vec{v} \times \vec{B}) \]
where \( q \) is the charge of the particle, \( \vec{v} \) is its velocity, and \( \vec{B} \) is the magnetic field.

2. **Analyzing the Angle of Velocity:**
If the velocity of the charged particle is at an angle \( \theta \) with respect to the magnetic field, where \( 0 < \theta < 90^\circ \), the motion can be decomposed into two components:
- A component parallel to the magnetic field (\( v_{\parallel} = v \cos(\theta) \))
- A component perpendicular to the magnetic field (\( v_{\perpendicular} = v \sin(\theta) \))

3. **Effects of the Perpendicular Component:**
The component of velocity perpendicular to the magnetic field will experience a magnetic force, causing the particle to move in a circular path in the plane perpendicular to the magnetic field. The radius of this circular motion is given by:
\[ r = \frac{mv_{\perpendicular}}{qB} \]
where \( m \) is the mass of the particle.

4. **Effects of the Parallel Component:**
The component of velocity parallel to the magnetic field will not experience any magnetic force, allowing the particle to continue moving in that direction at a constant speed.

5. **Resulting Motion:**
As a result, the combination of the circular motion (due to the perpendicular component) and the linear motion (due to the parallel component) leads to a helical path. The particle spirals around the magnetic field lines while moving forward along the direction of the field.

6. **Conclusion:**
Therefore, when the initial velocity of a charged particle is neither along nor perpendicular to the magnetic field, the path of the particle will be a **helical path**.

### Final Answer:
The orbit will be a **helical path**.