A charge q moves in a region where electric field E and the magnetic field B both exist, then the force on its is

Options

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

Answer

To solve the problem of finding the force on a charge \( q \) moving in an electric field \( E \) and a magnetic field \( B \), we can break it down into steps:

### Step-by-Step Solution:

1. **Identify the forces acting on the charge**:
- The charge \( q \) experiences two types of forces: one due to the electric field and another due to the magnetic field.

2. **Calculate the force due to the electric field**:
- The force \( F_e \) on the charge due to the electric field \( E \) is given by the formula:
\[ F_e = qE \]
- Here, \( q \) is the charge and \( E \) is the electric field strength.

3. **Calculate the force due to the magnetic field**:
- The force \( F_m \) on the charge moving with velocity \( v \) in a magnetic field \( B \) is given by the formula:
\[ F_m = q(v \times B) \]
- This is a vector product, meaning the direction of the force is determined by the right-hand rule, and \( v \) is the velocity of the charge.

4. **Combine the forces**:
- The net force \( F \) acting on the charge \( q \) is the sum of the electric force and the magnetic force:
\[ F = F_e + F_m \]
- Substituting the expressions for \( F_e \) and \( F_m \):
\[ F = qE + q(v \times B) \]

5. **Final expression for the net force**:
- Therefore, the total force on the charge \( q \) can be expressed as:
\[ F = qE + q(v \times B) \]

### Final Answer:
The force on the charge \( q \) moving in the presence of electric field \( E \) and magnetic field \( B \) is:
\[ F = qE + q(v \times B) \]