Force on a charged particle moving with velocity `vecv` subjected to a magnetic field is zero. This means:

Options

A. Angle between V and B is necessarily `90^@`
B. Angle between V and B can have any value other than `0^@ and 180^@`
C. Angle between V and B is either zero or `180^@`
D. Angle between V and B can have any value other than `90^@`

Explanation

To solve the question regarding the condition under which the force on a charged particle moving with velocity \( \vec{v} \) in a magnetic field \( \vec{B} \) is zero, we can follow these steps:

### Step 1: Understand the Formula for Magnetic Force
The force \( \vec{F} \) on a charged particle with charge \( q \) moving with velocity \( \vec{v} \) in a magnetic field \( \vec{B} \) is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
This equation indicates that the force is the cross product of the velocity vector and the magnetic field vector.

### Step 2: Analyze the Cross Product
The magnitude of the force can be expressed as:
\[ F = q v B \sin \theta \]
where \( \theta \) is the angle between the velocity vector \( \vec{v} \) and the magnetic field vector \( \vec{B} \).

### Step 3: Determine When Force is Zero
For the force \( F \) to be zero, the sine of the angle must be zero:
\[ \sin \theta = 0 \]
This occurs when:
\[ \theta = 0^\circ \quad \text{or} \quad \theta = 180^\circ \]
This means that the velocity vector \( \vec{v} \) is either parallel or anti-parallel to the magnetic field vector \( \vec{B} \).

### Step 4: Conclusion
Thus, the condition for the force on a charged particle to be zero is that the angle between the velocity vector \( \vec{v} \) and the magnetic field vector \( \vec{B} \) must be either \( 0^\circ \) or \( 180^\circ \).

### Final Answer
The correct option is:
**C: The angle between \( \vec{v} \) and \( \vec{B} \) is either \( 0^\circ \) or \( 180^\circ \).**

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