Lorentx force can be calculated by using the formula.

Options

A. `F=q(E+vxxB)`
B. `F=q(E-vxxB)`
C. `F=q(E+v.B)`
D. `F=q(Exxv+B)`

Answer

To calculate the Lorentz force acting on a charged particle moving in an electric and magnetic field, we can follow these steps:

### Step 1: Understand the Components of Lorentz Force
The Lorentz force (\( F \)) is the total force acting on a charged particle that has charge \( q \), moving with a velocity \( \mathbf{v} \), in the presence of an electric field \( \mathbf{E} \) and a magnetic field \( \mathbf{B} \).

### Step 2: Identify the Forces Acting on the Charged Particle
The Lorentz force can be expressed as the sum of the electric force and the magnetic force:
- The electric force (\( F_E \)) acting on the charged particle is given by:
\[ F_E = q \mathbf{E} \]
- The magnetic force (\( F_B \)) acting on the charged particle is given by:
\[ F_B = q (\mathbf{v} \times \mathbf{B}) \]

### Step 3: Combine the Forces
The total Lorentz force (\( F \)) is the sum of the electric and magnetic forces:
\[ F = F_E + F_B = q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \]

### Step 4: Factor Out the Charge
We can factor out the charge \( q \) from the equation:
\[ F = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]

### Conclusion
Thus, the formula for the Lorentz force is:
\[ F = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]

Based on the options provided, the correct answer is:
**Option A: \( F = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \)**

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