A charge moving with velocity `v` in `X`-direction is subjected to a field of magnetic induction in the negative `X`-direction. As a result, the charge will

Options

A. Remain unaffected
B. Start moving in a circular path `Y-Z` plane
C. Retard along `X`-axis
D. Move along a helical path around `X`- axis

Answer

To solve the question, we need to analyze the situation involving a charged particle moving in a magnetic field. The charge is moving with a velocity \( v \) in the positive \( X \)-direction, while the magnetic field \( B \) is directed in the negative \( X \)-direction. We will use the formula for the magnetic force acting on a charged particle moving in a magnetic field.

### Step-by-Step Solution:

1. **Identify the Direction of Motion and Magnetic Field**:
- The charge is moving in the positive \( X \)-direction.
- The magnetic field is in the negative \( X \)-direction.

2. **Use the Formula for Magnetic Force**:
- The magnetic force \( F \) on a charge \( q \) moving with velocity \( \vec{v} \) in a magnetic field \( \vec{B} \) is given by:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
- Here, \( \vec{v} \) is in the positive \( X \)-direction and \( \vec{B} \) is in the negative \( X \)-direction.

3. **Determine the Angle Between Velocity and Magnetic Field**:
- The angle \( \theta \) between the velocity vector \( \vec{v} \) and the magnetic field vector \( \vec{B} \) is \( 180^\circ \) since they are in opposite directions.

4. **Calculate the Sine of the Angle**:
- The sine of \( 180^\circ \) is:
\[ \sin(180^\circ) = 0 \]

5. **Calculate the Magnetic Force**:
- Substituting into the force equation:
\[ \vec{F} = q v B \sin(180^\circ) = q v B \cdot 0 = 0 \]
- Since the magnetic force \( \vec{F} \) is zero, the charge will not experience any force due to the magnetic field.

6. **Conclusion**:
- Since there is no magnetic force acting on the charge, it will remain unaffected by the magnetic field. Therefore, the correct answer is that the charge will remain unaffected.

### Final Answer:
The charge will remain unaffected.