A charged particle is moved along a magnetic field line. The magnetic force on the particle is

Options

A. along its velocity
B. opposite to its velocity
C. perpendicular to its velocity
D. zero.

Answer

To solve the problem, we need to analyze the situation of a charged particle moving in a magnetic field. Here's the step-by-step solution:

### Step 1: Understand the Magnetic Force Formula
The magnetic force \( F \) on a charged particle moving in a magnetic field is given by the formula:
\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector \( v \) and the magnetic field vector \( B \).

### Step 2: Analyze the Direction of Motion
In this case, it is given that the charged particle is moving along the magnetic field lines. This means that the direction of the velocity \( v \) of the particle is the same as the direction of the magnetic field \( B \).

### Step 3: Determine the Angle \( \theta \)
Since the particle is moving along the magnetic field lines, the angle \( \theta \) between the velocity \( v \) and the magnetic field \( B \) is:
\[ \theta = 0^\circ \]

### Step 4: Calculate the Magnetic Force
Substituting \( \theta = 0^\circ \) into the magnetic force formula:
\[ F = q \cdot v \cdot B \cdot \sin(0^\circ) \]
Since \( \sin(0^\circ) = 0 \), we have:
\[ F = q \cdot v \cdot B \cdot 0 = 0 \]

### Step 5: Conclusion
The magnetic force on the charged particle moving along the magnetic field lines is:
\[ F = 0 \]

Thus, the answer to the question is that the magnetic force on the particle is **zero**.

---