Assertion: Magnetic field can always accelerate the charged particle, if it is not moving, parallel or antiparallel to the magnetic field.
Reason: When the velocity of a charged particle makes an angle other than `0^(@) " or " 180^(@)` , magnetic force is nonzero.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion .
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the question, we need to analyze the assertion and reason provided:

### Assertion:
Magnetic field can always accelerate the charged particle, if it is not moving parallel or antiparallel to the magnetic field.

### Reason:
When the velocity of a charged particle makes an angle other than \(0^\circ\) or \(180^\circ\), the magnetic force is non-zero.

### Step-by-Step Solution:

1. **Understanding Magnetic Force**:
The magnetic force (\(F_B\)) acting on a charged particle moving in a magnetic field is given by the equation:
\[ F_B = Q \cdot (v \times B) \]
where \(Q\) is the charge, \(v\) is the velocity vector of the particle, and \(B\) is the magnetic field vector.

2. **Magnitude of Magnetic Force**:
The magnitude of the magnetic force can be expressed as:
\[ |F_B| = Q \cdot v \cdot B \cdot \sin(\theta) \]
where \(\theta\) is the angle between the velocity vector (\(v\)) and the magnetic field vector (\(B\)).

3. **Analyzing Angles**:
- If \(\theta = 0^\circ\) (parallel to the magnetic field) or \(\theta = 180^\circ\) (antiparallel to the magnetic field), then \(\sin(0^\circ) = 0\) and \(\sin(180^\circ) = 0\). This results in:
\[ |F_B| = 0 \]
- Thus, the magnetic force is zero when the charged particle moves parallel or antiparallel to the magnetic field.

4. **Non-zero Magnetic Force**:
- If the angle \(\theta\) is anything other than \(0^\circ\) or \(180^\circ\) (i.e., \(0 < \theta < 180\)), then \(\sin(\theta)\) is non-zero, leading to a non-zero magnetic force:
\[ |F_B| \neq 0 \]
- This means that the charged particle will experience a magnetic force, which can cause it to accelerate.

5. **Conclusion about Assertion and Reason**:
- The assertion states that a magnetic field can always accelerate a charged particle if it is not moving parallel or antiparallel to the magnetic field. This is true because a non-zero magnetic force implies a non-zero acceleration.
- The reason correctly explains that the magnetic force is non-zero when the angle is not \(0^\circ\) or \(180^\circ\).

6. **Final Evaluation**:
Both the assertion and reason are correct, and the reason provides a correct explanation for the assertion.

### Final Answer:
Both assertion and reason are correct, and the reason is the correct explanation of the assertion.

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