Select the incorrect option regarding Lorentz force.

Options

A. In presence of electric field `vecE` (r) and magnetic field `vecB` (r), the force on a moving electric charge is:
`vecF = q[vecE (r) + vecv xx vecB (r)]`
B. The force due to magnetic field on a negative charge is opposite to that on a positive charge
C. The force due to magnetic field becomes zero when velocity and magnetic field are parallel or antiparallel
D. For a static charge the magnetic force is maximum

Explanation

To solve the question regarding the incorrect option related to the Lorentz force, we need to analyze the statements provided and determine which one is false based on our understanding of the Lorentz force law.

### Step-by-Step Solution:

1. **Understanding Lorentz Force**:
The Lorentz force \( \mathbf{F} \) acting on a charge \( Q \) moving with velocity \( \mathbf{V} \) in an electric field \( \mathbf{E} \) and a magnetic field \( \mathbf{B} \) is given by the equation:
\[ \mathbf{F} = Q(\mathbf{E} + \mathbf{V} \times \mathbf{B}) \]
Here, \( \mathbf{E} \) is the electric field vector, \( \mathbf{V} \) is the velocity vector of the charge, and \( \mathbf{B} \) is the magnetic field vector.

2. **Analyzing Each Option**:
- **Option 1**: "The force on a moving electric charge in the presence of electric and magnetic fields is given by \( \mathbf{F} = Q(\mathbf{E} + \mathbf{V} \times \mathbf{B}) \)".
- This statement is **true** as it directly follows from the definition of the Lorentz force.

- **Option 2**: "The force due to the magnetic field on a negative charge is opposite to that on a positive charge".
- This statement is **true**. The direction of the force is determined by the sign of the charge; hence, a negative charge will experience a force in the opposite direction compared to a positive charge.

- **Option 3**: "The force due to a magnetic field becomes zero when velocity and magnetic field are parallel or anti-parallel".
- This statement is **true**. When the velocity \( \mathbf{V} \) and magnetic field \( \mathbf{B} \) are parallel or anti-parallel, the angle \( \theta \) between them is either 0° or 180°, making \( \sin \theta = 0 \). Thus, the magnetic force becomes zero.

- **Option 4**: "For a static charge, the magnetic force is maximum".
- This statement is **incorrect**. For a static charge (where the velocity \( \mathbf{V} = 0 \)), the magnetic force is zero, not maximum. The maximum magnetic force occurs when the charge is moving perpendicular to the magnetic field.

3. **Conclusion**:
Based on the analysis, the incorrect option regarding the Lorentz force is:
- **Option 4**: "For a static charge, the magnetic force is maximum".