Kinetic energy of a charged particle is zero at time `t_(0)`. K at time 2 `t_(0)`. 2K at time 3 `t_(0)`. It remains constant (i.e.2K) upto 4 `t_(0)`. Choose the correct option.

Options

A. Only electric field is present between a time interval from `t_(0)` to 2 `t_(0)`
B. No field is present between time interal from interval from 3 `t_(0)` to 4 `t_(0)`
C. Both (a) and (b) are correct
D. Both (a) and (b) are wrong

Answer

To solve the problem, we need to analyze the kinetic energy of the charged particle at different time intervals and understand the implications regarding the presence of electric and magnetic fields.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy at Different Times:**
- At time \( t_0 \), the kinetic energy \( KE = 0 \).
- At time \( 2t_0 \), the kinetic energy \( KE = K \).
- At time \( 3t_0 \), the kinetic energy \( KE = 2K \).
- At time \( 4t_0 \), the kinetic energy remains constant at \( KE = 2K \).

2. **Analyzing the Change in Kinetic Energy:**
- From \( t_0 \) to \( 2t_0 \), the kinetic energy increases from \( 0 \) to \( K \). This indicates that work is done on the particle, which suggests the presence of an electric field.
- From \( 2t_0 \) to \( 3t_0 \), the kinetic energy increases from \( K \) to \( 2K \). This is again indicative of work being done, likely due to the electric field.
- From \( 3t_0 \) to \( 4t_0 \), the kinetic energy remains constant at \( 2K \). This suggests that no net work is being done on the particle during this interval.

3. **Determining the Presence of Electric and Magnetic Fields:**
- The presence of an electric field is confirmed between \( t_0 \) and \( 3t_0 \) because the kinetic energy is changing.
- From \( 3t_0 \) to \( 4t_0 \), since the kinetic energy is constant, it implies that there is no electric field doing work on the particle. However, a magnetic field could still be present since it does not do work on the particle and does not change its kinetic energy.

4. **Conclusion on the Statements:**
- The statement that "only electric field is present between the time interval from \( t_0 \) to \( 2t_0 \)" is incorrect because while the electric field is present, a magnetic field could also be present without affecting kinetic energy.
- The statement that "no field is present between the time interval from \( 3t_0 \) to \( 4t_0 \)" is also incorrect because a magnetic field could still be present.

5. **Final Answer:**
- Therefore, both statements A and B are incorrect, leading us to conclude that the correct option is D: "Both A and B are wrong."