A charged particle describes a circle under the influence of the magnetic field. The quantities that remain constant are
i) K. E ii) Velocity
iii) Time period iv) Momentum

Options

A. Only i & iii are true
B. Only i & iv are true
C. Only i,ii&iii are true
D. All are true

Answer

To determine which quantities remain constant for a charged particle moving in a circular path under the influence of a magnetic field, we can analyze each option step by step.

### Step-by-Step Solution:

1. **Kinetic Energy (K.E.)**:
- The work done on the charged particle by the magnetic field is zero because the magnetic force is always perpendicular to the velocity of the particle.
- Since work done is zero, the change in kinetic energy is also zero. Therefore, the kinetic energy remains constant.
- **Conclusion**: K.E. is constant.

2. **Velocity**:
- The velocity of the particle is a vector quantity that has both magnitude and direction. While the magnitude of the velocity (speed) may remain constant, the direction of the velocity continuously changes as the particle moves in a circular path.
- Since velocity is defined as a vector, and its direction is changing, the velocity itself is not constant.
- **Conclusion**: Velocity is not constant.

3. **Time Period (T)**:
- The time period of the circular motion can be derived from the relationship between the radius (r), mass (m), charge (q), and magnetic field (B).
- The time period T is given by the formula \( T = \frac{2\pi m}{qB} \). Here, m, q, and B are constants, which means T is also constant.
- **Conclusion**: Time period is constant.

4. **Momentum (p)**:
- Momentum is given by the product of mass and velocity, \( p = mv \). Although mass remains constant, the velocity is changing due to the changing direction.
- Since velocity is not constant, the momentum will also not be constant.
- **Conclusion**: Momentum is not constant.

### Final Answer:
The quantities that remain constant are:
- Kinetic Energy (K.E.)
- Time Period (T)

Thus, the correct options are i) K.E. and iii) Time Period.