Lorentz force

Options

A. `q[vecE+(vecBxxvecv)]`
B. `q[vecE+(vecvxxvecB)]`
C. `q(vecvxxvecB)`
D. `qvecE`

Answer

### Step-by-Step Solution for Lorentz Force

**Step 1: Understanding Lorentz Force**
The Lorentz force is the force experienced by a charged particle moving in an electromagnetic field. It is a combination of the electric force and the magnetic force acting on the particle.

**Step 2: Formula for Lorentz Force**
The Lorentz force \( \mathbf{F} \) can be expressed mathematically as:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \]
where:
- \( \mathbf{F} \) is the total force acting on the charge,
- \( q \) is the charge of the particle,
- \( \mathbf{E} \) is the electric field,
- \( \mathbf{v} \) is the velocity of the charge,
- \( \mathbf{B} \) is the magnetic field,
- \( \times \) denotes the cross product.

**Step 3: Components of the Lorentz Force**
- **Electric Force**: The force due to the electric field is given by \( \mathbf{F}_E = q \mathbf{E} \).
- **Magnetic Force**: The force due to the magnetic field is given by \( \mathbf{F}_B = q (\mathbf{v} \times \mathbf{B}) \).

**Step 4: Interpretation of the Cross Product**
The term \( \mathbf{v} \times \mathbf{B} \) indicates that the magnetic force is dependent on the direction of the velocity of the charge relative to the magnetic field. The direction of the magnetic force can be determined using the right-hand rule.

**Step 5: Conclusion**
The Lorentz force is crucial in understanding the motion of charged particles in electric and magnetic fields, and it plays a significant role in various applications in electromagnetism.