Which of the following statements is correct?

Options

A. If the moving charged particle enters into a region of magnetic field form outside, it does not complete a circular path.
B. If a moving charged particle traces a helical path in a uniform magnetic field, the axis of the helix is parallel to the magnetic field.
C. The power associated with the force exerted by a magnetic field on a moving charged particle moving charged particle is always equal to zero.
D. If in a region a uniform magnetic field and a uniform electric field both exist, a charged particle moving in this region cannot trace a circular path.

Explanation

To solve the question regarding which of the statements is correct, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Statement:** If a moving charged particle enters into a region of magnetic field from outside, it does not complete a circular path.

- When a charged particle enters a magnetic field perpendicularly, it experiences a magnetic force that acts perpendicular to its velocity. This force causes the particle to move in a circular path.
- However, if the particle enters from outside the magnetic field, it will only complete a semicircular path before exiting the field, as it will not have enough distance to complete a full circle.

**Conclusion for Option 1:** This statement is correct.

### Step 2: Analyze Option 2
**Statement:** If a moving charged particle traces a helical path in a uniform magnetic field, the axis of the helix is parallel to the magnetic field.

- When a charged particle moves at an angle to the magnetic field, it has two components of velocity: one parallel to the magnetic field (v cos θ) and one perpendicular (v sin θ).
- The component parallel to the field allows the particle to move forward, while the perpendicular component causes it to move in a circular motion. Therefore, the path traced is indeed helical, and the axis of the helix is parallel to the magnetic field.

**Conclusion for Option 2:** This statement is correct.

### Step 3: Analyze Option 3
**Statement:** The power associated with the force exerted by a magnetic field on a moving charged particle is always equal to zero.

- The magnetic force acting on a charged particle is always perpendicular to its velocity. Since power is defined as the rate of doing work (P = F · v), and the work done by a force that is perpendicular to the direction of motion is zero, the power associated with the magnetic force is indeed zero.

**Conclusion for Option 3:** This statement is correct.

### Step 4: Analyze Option 4
**Statement:** In a region of uniform magnetic field and uniform electric field, a charged particle moving in the region cannot trace a circular path.

- In the presence of both electric and magnetic fields, the electric field exerts a force that changes the velocity of the charged particle. The radius of the circular path is given by r = mv/qB. If the velocity (v) changes due to the electric field, the radius (r) also changes, preventing the particle from tracing a complete circular path.

**Conclusion for Option 4:** This statement is correct.

### Final Conclusion
All four options are correct statements regarding the behavior of charged particles in magnetic and electric fields.

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