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:
(1.)angle between v and B is necessery 90 ∘
(2.)angle between v and B can have any value other than 90 ∘
(3.)angle between v and B can have any value other than zero and 180 ∘
(4.)angle between v and B is either zero or 180 ∘

Options

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

Answer

To solve the question, we need to analyze the relationship between the force acting on a charged particle moving in a magnetic field and the angles involved.

### Step-by-Step Solution:

1. **Understanding the Force on a Charged Particle**:
The force \( \vec{F} \) on a charged particle moving with velocity \( \vec{V} \) in a magnetic field \( \vec{B} \) is given by the equation:
\[ \vec{F} = q (\vec{V} \times \vec{B}) \]
where \( q \) is the charge of the particle.

2. **Magnitude of the Force**:
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 \( \vec{B} \).

3. **Condition for Non-Zero Force**:
For the force \( F \) to be non-zero, the sine term must also be non-zero:
\[ \sin \theta \neq 0 \]
This condition implies that \( \theta \) cannot be \( 0^\circ \) or \( 180^\circ \) because:
- \( \sin 0^\circ = 0 \)
- \( \sin 180^\circ = 0 \)

4. **Conclusion on the Angle \( \theta \)**:
Since \( \theta \) cannot be \( 0^\circ \) or \( 180^\circ \), it can take any other value. This leads us to conclude that the angle between \( \vec{V} \) and \( \vec{B} \) can be any angle except \( 0^\circ \) or \( 180^\circ \).

5. **Identifying the Correct Option**:
Among the given options:
- (1) Angle between \( \vec{V} \) and \( \vec{B} \) is necessary \( 90^\circ \) - Incorrect
- (2) Angle between \( \vec{V} \) and \( \vec{B} \) can have any value other than \( 90^\circ \) - Incorrect
- (3) Angle between \( \vec{V} \) and \( \vec{B} \) can have any value other than \( 0^\circ \) and \( 180^\circ \) - Correct
- (4) Angle between \( \vec{V} \) and \( \vec{B} \) is either \( 0^\circ \) or \( 180^\circ \) - Incorrect

Thus, the correct answer is option (3): The angle between \( \vec{V} \) and \( \vec{B} \) can have any value other than \( 0^\circ \) and \( 180^\circ \).