An electric charge q is moving with a velocity w in the direction of a magnetic field B. The magnetic force acting on the charge is

Options

A. `q vB`
B. zero
C. `q/(vB)`
D. `v/(qB)`

Answer

To find the magnetic force acting on a moving charge in a magnetic field, we can use the Lorentz force equation. The magnetic force \( F \) on a charge \( q \) moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) is given by:

\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Charge \( q \)
- Velocity \( \mathbf{v} \) (in the direction of the magnetic field \( \mathbf{B} \))
- Magnetic field \( \mathbf{B} \)

2. **Understand the Direction of Motion:**
- The charge is moving in the same direction as the magnetic field. This means that the angle \( \theta \) between the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \) is \( 0^\circ \).

3. **Apply the Lorentz Force Formula:**
- The formula for magnetic force is \( \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \).
- The cross product \( \mathbf{v} \times \mathbf{B} \) can be calculated using the sine of the angle between the two vectors:
\[ |\mathbf{v} \times \mathbf{B}| = |\mathbf{v}| |\mathbf{B}| \sin(\theta) \]

4. **Calculate the Cross Product:**
- Since \( \theta = 0^\circ \), we have:
\[ \sin(0^\circ) = 0 \]
- Therefore, the cross product becomes:
\[ |\mathbf{v} \times \mathbf{B}| = |\mathbf{v}| |\mathbf{B}| \cdot 0 = 0 \]

5. **Determine the Magnetic Force:**
- Substituting back into the Lorentz force equation:
\[ \mathbf{F} = q \cdot 0 = 0 \]
- Thus, the magnetic force acting on the charge is:
\[ \mathbf{F} = 0 \]

### Conclusion:
The magnetic force acting on the charge \( q \) moving in the direction of the magnetic field \( \mathbf{B} \) is zero.