Statement 1: A magnetic field independent of time can change the velocity of a charged particle.
Statement 2: It is not possible to change the velocity of a particle in a magnetic field as magnetic field does no work on the charged particle.

Options

A. If both statement 1 and statement 2 are ture, statement 2 is the correct explanation of statement 1.
B. If both statement 1 and statement 2 are ture, statement 2 is not the correct explanation of statement 1.
C. If statement 1 is true, statement 2 is false.
D. If statement 1 is false, statement 2 is true.

Explanation

To analyze the two statements regarding the effect of a magnetic field on a charged particle, let's break down the concepts step-by-step.

### Step 1: Understanding Statement 1
**Statement 1** claims that a magnetic field independent of time can change the velocity of a charged particle.

- A magnetic field exerts a force on a charged particle given by the Lorentz force equation:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the particle, \( \mathbf{v} \) is its velocity, and \( \mathbf{B} \) is the magnetic field.

- This force is always perpendicular to the velocity of the charged particle. Therefore, while the magnetic field does not do work (since work is defined as force along the direction of displacement), it can change the direction of the velocity vector.

**Conclusion for Statement 1**: The statement is **true** because the magnetic field can change the direction of the velocity, which means the velocity vector changes even if the speed (magnitude of velocity) remains constant.

### Step 2: Understanding Statement 2
**Statement 2** claims that it is not possible to change the velocity of a particle in a magnetic field because the magnetic field does no work on the charged particle.

- As discussed, the magnetic field does not do work on the charged particle; however, it can change the direction of the velocity vector.

- Velocity is a vector quantity that depends on both speed and direction. Since the direction of the velocity changes due to the magnetic force, the velocity itself changes even though the speed remains constant.

**Conclusion for Statement 2**: The statement is **false** because, although the magnetic field does no work, it can still change the velocity by altering its direction.

### Final Conclusion
- **Statement 1 is true**: A magnetic field can change the velocity of a charged particle by changing its direction.
- **Statement 2 is false**: It is possible to change the velocity of a particle in a magnetic field, despite the magnetic field doing no work.

### Summary
- **Correct Answer**: Statement 1 is true; Statement 2 is false.

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