If a chraged particle at rest experiences no electromagnetic force,
(i) the electric field must be zero
(ii) the magnetic field must be zero
(iii) the electric field may or may not be zero
(iv) the magnetic field may or may not be zero

Options

A. The electric field must be zero
B. The magnetic field must be zero
C. The electric field may or may not be zero
D. All of these

Answer

To solve the question, we need to analyze the situation where a charged particle is at rest and experiences no electromagnetic force. We will use the Lorentz force equation to understand the implications of this scenario.

### Step-by-step Solution:

1. **Understanding the Lorentz Force Equation**:
The Lorentz force \( F \) acting on a charged particle is given by the equation:
\[ F = qE + q(v \times B) \]
where:
- \( F \) is the total force on the charged particle,
- \( q \) is the charge of the particle,
- \( E \) is the electric field,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field.

2. **Analyzing the Given Condition**:
The problem states that the charged particle is at rest. This means that the velocity \( v = 0 \). Therefore, the magnetic force term \( q(v \times B) \) becomes zero:
\[ F = qE + q(0 \times B) = qE \]
Hence, the total force on the particle is solely due to the electric field.

3. **Condition of No Force**:
Since it is given that the particle experiences no electromagnetic force, we have:
\[ F = 0 \]
This implies:
\[ qE = 0 \]
Since \( q \) (the charge) is not zero, we conclude that:
\[ E = 0 \]
Therefore, the electric field must be zero for the particle to experience no force.

4. **Evaluating the Options**:
- **Option (i)**: The electric field must be zero. **(True)**
- **Option (ii)**: The magnetic field must be zero. **(False)** - The magnetic field can be present, but it does not affect the particle since it is at rest.
- **Option (iii)**: The electric field may or may not be zero. **(False)** - We established that the electric field must be zero.
- **Option (iv)**: The magnetic field may or may not be zero. **(True)** - The magnetic field's presence does not affect the force on the particle since it is at rest.

### Conclusion:
The correct options are:
- (i) The electric field must be zero.
- (iv) The magnetic field may or may not be zero.