A charge q moves region in a electric field E and the magnetic field B both exist, then the force on its is:
(1.)q ( v × B )
(2.)q E + q ( v × B )
(3.)q B + q ( B × v )
(4.)q B + q ( B × v )

Options

A. `q(vxxB)`
B. `qE+q(vxxB)`
C. `qB+q(Bxxv)`
D. `qB+q(Exxv)`

Answer

To solve the problem, we need to determine the total force acting on a charge \( q \) that is moving in the presence of both an electric field \( \mathbf{E} \) and a magnetic field \( \mathbf{B} \).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Charge**:
- The force acting on a charge \( q \) due to an electric field \( \mathbf{E} \) is given by:
\[ \mathbf{F}_E = q \mathbf{E} \]
- The force acting on the charge \( q \) due to a magnetic field \( \mathbf{B} \) when the charge is moving with a velocity \( \mathbf{v} \) is given by:
\[ \mathbf{F}_M = q (\mathbf{v} \times \mathbf{B}) \]

2. **Combine the Forces**:
- The total force \( \mathbf{F} \) acting on the charge \( q \) is the vector sum of the electric force and the magnetic force:
\[ \mathbf{F} = \mathbf{F}_E + \mathbf{F}_M \]
- Substituting the expressions for \( \mathbf{F}_E \) and \( \mathbf{F}_M \):
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \]

3. **Final Expression for the Total Force**:
- Therefore, the total force acting on the charge \( q \) in the presence of both electric and magnetic fields is:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \]

4. **Identify the Correct Option**:
- From the options provided, the correct expression for the total force is:
- (2) \( q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \)

### Conclusion:
The correct answer is option (2): \( q \mathbf{E} + q (\mathbf{v} \times \mathbf{B}) \).