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 of a charged particle moving along a magnetic field line, we can follow these steps:

### Step 1: Understand the Magnetic Force Equation
The magnetic force \( F \) on a charged particle moving in a magnetic field is given by the equation:
\[ F = q (\mathbf{v} \times \mathbf{B}) \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( \mathbf{v} \) is the velocity vector of the particle,
- \( \mathbf{B} \) is the magnetic field vector.

### Step 2: Analyze the Direction of Motion
In this case, the problem states that the charged particle is moving along the magnetic field line. This means that the direction of the velocity vector \( \mathbf{v} \) is the same as the direction of the magnetic field vector \( \mathbf{B} \).

### Step 3: Determine the Angle Between Vectors
The angle \( \theta \) between the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \) is crucial for calculating the sine component in the magnetic force equation. Since the particle is moving along the field line, the angle \( \theta \) is:
\[ \theta = 0^\circ \]

### Step 4: Calculate the Sine of the Angle
Using the sine function:
\[ \sin(0^\circ) = 0 \]

### Step 5: Substitute into the Magnetic Force Equation
Substituting this value back into the magnetic force equation, we have:
\[ F = q |\mathbf{v}| |\mathbf{B}| \sin(0^\circ) = q |\mathbf{v}| |\mathbf{B}| \cdot 0 = 0 \]

### Conclusion
The magnetic force \( F \) on the charged particle moving along the magnetic field line is:
\[ F = 0 \]

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

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