When a charged particle moving with velocity `vec v` is subjected to a magnetic field of induction `vec B`, the force on it is non-zero. This implies that:

Options

A. angle between `vec(v)` and `vec(B)` is necessarily `90^(@)`
B. angle between `vec(v)` and `vec(B)` can have any value other then `90^(@)`
C. angle between `vec(v)` and `vec(B)` can have any value other than zero and `180^(@)`
D. angle between `vec(v)` and `vec(B)` is either zero or `180^(@)`

Explanation

To solve the question regarding the force on a charged particle moving in a magnetic field, we can follow these steps:

### Step 1: Understand the Force on a Charged Particle
The force \( \vec{F} \) acting 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 dependent on the cross product of the velocity and the magnetic field vectors.

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

### Step 3: Determine Conditions for Non-Zero Force
For the force \( F \) to be non-zero, the sine function must also be non-zero. This occurs when:
\[ \sin \theta \neq 0 \]
The sine function is zero at angles \( \theta = 0^\circ \) and \( \theta = 180^\circ \). Therefore, the force will be non-zero when:
\[ \theta \neq 0^\circ \quad \text{and} \quad \theta \neq 180^\circ \]

### Step 4: Conclusion
Since the problem states that the force on the charged particle is non-zero, this implies that the angle \( \theta \) between the velocity vector \( \vec{v} \) and the magnetic field vector \( \vec{B} \) can take any value except for \( 0^\circ \) and \( 180^\circ \).

Thus, the correct implication is:
- The angle between \( \vec{v} \) and \( \vec{B} \) can have any values other than \( 0^\circ \) and \( 180^\circ \).

### Final Answer
The implication is that the angle between \( \vec{v} \) and \( \vec{B} \) can have any values other than \( 0^\circ \) and \( 180^\circ \).

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