An electron is fired parallel to uniform electric and uniform magnetic field acting simultaneously and in the same direction. The electron

Options

A. Moves along a circular path
B. Moves along a parabolic path
C. Loses K.E
D. Gains K.E

Answer

To solve the problem, we need to analyze the forces acting on the electron when it is fired parallel to both a uniform electric field (E) and a uniform magnetic field (B), both acting in the same direction.

### Step-by-step Solution:

1. **Identify the Direction of Forces**:
- The electron is fired with a velocity \( v \) in the same direction as the electric field \( E \) and the magnetic field \( B \).

2. **Calculate the Magnetic Force**:
- The magnetic force \( F_B \) on a charged particle is given by the equation:
\[ F_B = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the particle (for an electron, \( q = -e \)), \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector.
- Since the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \) are in the same direction, the cross product \( \mathbf{v} \times \mathbf{B} \) will be zero:
\[ F_B = 0 \]

3. **Calculate the Electric Force**:
- The electric force \( F_E \) on the electron is given by:
\[ F_E = qE \]
- Since the electron has a negative charge, the direction of the electric force will be opposite to the direction of the electric field:
\[ F_E = -eE \]

4. **Determine the Net Force**:
- The only force acting on the electron is the electric force \( F_E \), which acts in the opposite direction to the velocity of the electron. Therefore, the net force acting on the electron is:
\[ F_{net} = F_E = -eE \]

5. **Effect on Velocity and Kinetic Energy**:
- Since the electric force acts opposite to the direction of the velocity, it will cause the velocity of the electron to decrease over time.
- As the velocity decreases, the kinetic energy of the electron will also decrease.

6. **Path of the Electron**:
- The electron will not experience any magnetic force, and since the electric force is constant and acts in the opposite direction to its motion, the path of the electron will be a straight line, but with decreasing speed.

### Conclusion:
The electron will move in a straight line but will experience a decrease in speed due to the electric force acting against its motion.