An electron travels through a region of space with no acceleration . Which one of the following statements is the best conclusion ?

Options

A. Both E and B must be zero in that region
B. E must be zero, but B might be non-zero in that region
C. E and B might both be non-zero , but they be mutually perpendicular
D. B must be zero, but E mightbe non-zero in that region

Answer

To solve the problem, we need to analyze the situation of an electron traveling through a region of space with no acceleration. Here's a step-by-step breakdown of the reasoning:

### Step 1: Understand the Implications of No Acceleration
- The statement mentions that the electron is traveling with no acceleration. This implies that the net force acting on the electron is zero according to Newton's first law of motion.

### Step 2: Apply Newton's Second Law
- According to Newton's second law, \( F = ma \). If the acceleration \( a = 0 \), then the net force \( F \) must also be zero:
\[ F_{net} = 0 \]

### Step 3: Consider the Forces Acting on the Electron
- The forces acting on a charged particle like an electron in an electromagnetic field can be described by the Lorentz force equation:
\[ F = qE + q(v \times B) \]
where \( q \) is the charge of the electron, \( E \) is the electric field, \( v \) is the velocity of the electron, and \( B \) is the magnetic field.

### Step 4: Analyze the Conditions for Zero Net Force
- For the net force to be zero, the sum of the electric force and the magnetic force must equal zero:
\[ qE + q(v \times B) = 0 \]
This can be rearranged to show that:
\[ E = - (v \times B) \]

### Step 5: Determine the Relationship Between Electric and Magnetic Fields
- This equation indicates that the electric field \( E \) can be non-zero as long as it is equal in magnitude and opposite in direction to the magnetic force \( q(v \times B) \). Therefore, both \( E \) and \( B \) can exist simultaneously.

### Step 6: Evaluate the Given Options
- Now, we can evaluate the options provided in the question:
1. **Both E and B must be zero in that region.** - Incorrect, as \( E \) and \( B \) can be non-zero while satisfying the condition of no acceleration.
2. **E must be zero, but B might be non-zero in that region.** - Incorrect, as if \( E = 0 \), then the net force would not be zero unless \( B \) is also zero.
3. **E and B might both be non-zero.** - Correct, as they can exist simultaneously and still result in zero net force.
4. **B must be zero, but E might be non-zero in that region.** - Incorrect, as this would not satisfy the condition of zero net force.

### Conclusion
- The best conclusion is that **E and B might both be non-zero**, which corresponds to option 3.