Choose the correct statement

Options

A. It is possible for a current loop to stay without rotating in a uniform magnetic field
B. If a uniform magnetic field exists in a cubical region and zero outside then it is not possible to project a charged particle from outside into the field so that it describes a complete circle in the field
C. A moving charged particle can be accelerated by a magnetic field
D. All of these

Answer

To solve the question, we need to analyze each of the given statements and determine their correctness based on the principles of electromagnetism.

### Step-by-Step Solution:

1. **Analyze Option 1**:
- The statement claims that it is possible for a current loop to stay without rotating in a uniform magnetic field.
- A current loop in a magnetic field experiences a torque given by the formula \( \tau = \vec{m} \times \vec{B} \), where \( \vec{m} \) is the magnetic moment and \( \vec{B} \) is the magnetic field.
- If the angle \( \theta \) between \( \vec{m} \) and \( \vec{B} \) is 0 degrees (i.e., they are aligned), the torque \( \tau \) becomes zero.
- Therefore, the current loop will not rotate. This statement is **correct**.

2. **Analyze Option 2**:
- The statement discusses a uniform magnetic field existing in a cubical region with zero field outside.
- If a charged particle is projected from outside into this magnetic field, it will not be able to describe a complete circle because the magnetic field does not extend beyond the cube.
- Once the particle exits the magnetic field, it will no longer experience the magnetic force required to keep it in circular motion. Hence, this statement is also **correct**.

3. **Analyze Option 3**:
- The statement asserts that a moving charged particle can be accelerated by a magnetic field.
- A magnetic field exerts a force on a charged particle given by \( F = q(\vec{v} \times \vec{B}) \). This force can change the direction of the particle's velocity, which is a form of acceleration.
- However, it is important to note that while the magnetic field can change the direction of the particle's motion, it does not do work on the particle (as the force is always perpendicular to the velocity). Thus, the speed remains constant, but the direction changes. This statement is **correct**.

4. **Conclusion**:
- Since all three options (1, 2, and 3) are correct, the implication is that option 4 (which states that all previous options are correct) must also be correct. Thus, the correct answer is option 4.

### Final Answer:
All three statements are correct, therefore option 4 is the correct choice.

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