A charge particle travels along a straight line with a speed v in region where both electric field E and magnetic field b are present.It follows that

Options

A. `|E|=|B|` and the two field are perpendicular
B. `|E|=v|B|` and the two field are perpendicular
C. `|B|=v|E|` and the two field are parallel
D. `|B|=v|E|` and the two fields are perpendicular

Answer

To solve the problem of a charged particle traveling along a straight line in the presence of both electric and magnetic fields, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Forces Acting on the Charged Particle**:
- The charged particle experiences two forces: the electric force (\( F_E \)) and the magnetic force (\( F_B \)).
- The electric force is given by:
\[ F_E = Q \cdot E \]
- The magnetic force is given by:
\[ F_B = Q \cdot (v \times B) \]

2. **Set Up the Condition for Straight-Line Motion**:
- For the charged particle to move in a straight line, the net force acting on it must be zero:
\[ F_E + F_B = 0 \]
- This implies:
\[ Q \cdot E + Q \cdot (v \times B) = 0 \]

3. **Simplify the Equation**:
- Since \( Q \) is not zero, we can divide the entire equation by \( Q \):
\[ E + (v \times B) = 0 \]
- Rearranging gives:
\[ E = - (v \times B) \]

4. **Analyze the Magnitudes**:
- Taking magnitudes on both sides, we have:
\[ |E| = |v| \cdot |B| \cdot \sin(\theta) \]
- Here, \( \theta \) is the angle between the velocity vector \( v \) and the magnetic field vector \( B \).

5. **Determine the Relationship Between the Fields**:
- For the charged particle to move in a straight line, the electric field \( E \) must be equal in magnitude to the magnetic force, which implies that the two fields are perpendicular to each other:
\[ |E| = |v| \cdot |B| \]
- This indicates that the electric field \( E \) is perpendicular to the magnetic field \( B \).

6. **Conclusion**:
- Therefore, we conclude that the magnitude of the electric field \( E \) is equal to the product of the speed \( v \) of the charged particle and the magnitude of the magnetic field \( B \), and the two fields are perpendicular.

### Final Answer:
The correct relationship is:
\[ |E| = |v| \cdot |B| \quad \text{and the fields are perpendicular.} \]