An electron is projected with certain velocity into an electric field in a direction opposite to the field. Then it is

Options

A. accelerated
B. retarded
C. neigther accelerated nor retarded
D. either accelerated or retarded

Answer

To solve the problem of an electron projected into an electric field in a direction opposite to the field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Electric Field Direction**:
- Let's denote the direction of the electric field as \(E\). The electric field exerts a force on charged particles. For a positive charge, the force is in the direction of the electric field, while for a negative charge (like an electron), the force is in the opposite direction.

2. **Determine the Force on the Electron**:
- The force \(F\) acting on the electron can be calculated using the formula:
\[ F = qE \]
where \(q\) is the charge of the electron. Since the charge of an electron is negative (\(q = -e\)), the force on the electron will be:
\[ F = -eE \]
- This indicates that the force acting on the electron is in the direction opposite to the electric field.

3. **Analyze the Motion of the Electron**:
- The electron is projected with an initial velocity \(V\) in the direction opposite to the electric field. Since the force acting on the electron is also in the direction opposite to the electric field, it will experience a deceleration (or retardation).

4. **Calculate the Acceleration**:
- The acceleration \(a\) of the electron can be calculated using Newton's second law:
\[ a = \frac{F}{m} \]
where \(m\) is the mass of the electron. Substituting the expression for force:
\[ a = \frac{-eE}{m} \]
- The negative sign indicates that the acceleration is in the direction opposite to the initial velocity of the electron.

5. **Conclusion**:
- Since the electron is moving in the opposite direction of the electric field and the force (and thus acceleration) is also in the opposite direction of its initial velocity, the electron will be decelerated (retarded) as it moves through the electric field.

### Final Answer:
The electron will be retarded (decelerated) as it moves in the electric field.

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