A charged particle would continue to move with a constant velocity in a region wherein, which of the following conditions is not correct?

Options

A. `E=0, B ne 0`
B. `E ne 0, B ne 0`
C. `E ne 0, B =0`
D. `E=0, B=0`

Answer

To solve the question regarding the conditions under which a charged particle continues to move with a constant velocity, we can follow these steps:

### Step 1: Understand the Concept of Constant Velocity
A charged particle moves with a constant velocity when the net force acting on it is zero. According to Newton's first law of motion, an object will maintain its state of rest or uniform motion unless acted upon by a net external force.

### Step 2: Identify the Forces Acting on the Charged Particle
The forces acting on a charged particle in an electric field (E) and a magnetic field (B) are described by the Lorentz force equation:
\[ F = QE + Q(V \times B) \]
where:
- \( F \) is the total force,
- \( Q \) is the charge of the particle,
- \( E \) is the electric field,
- \( V \) is the velocity of the particle,
- \( B \) is the magnetic field.

### Step 3: Set the Net Force to Zero for Constant Velocity
For the charged particle to move with a constant velocity, the net force must be zero:
\[ QE + Q(V \times B) = 0 \]

### Step 4: Analyze the Conditions
From the equation \( QE + Q(V \times B) = 0 \), we can deduce the conditions:
1. If \( QE = 0 \), then either \( Q = 0 \) (the particle is uncharged) or \( E = 0 \) (no electric field present).
2. If \( Q(V \times B) = 0 \), then either \( Q = 0 \) (the particle is uncharged) or \( V \times B = 0 \) (the velocity is parallel to the magnetic field).

### Step 5: Determine the Incorrect Condition
The question asks for the condition that is **not correct** for the particle to maintain constant velocity. The incorrect condition would be any situation where the net force is not zero, meaning there is a non-zero electric or magnetic force acting on the particle.

### Conclusion
The charged particle will not continue to move with a constant velocity if there is a net force acting on it, which occurs when either the electric field or the magnetic field is present and not balanced by the motion of the particle.