A uniform electric field and a uniform magneitc field exist in a region in the same direction An electron is projected with velocity pointed in the same direction the electron will

Options

A. be deflected to the left without increase in speed
B. be deflected to the right without increase in speed
C. not be deflected but its speed will decrease
D. not be deflected but its speed will increase

Answer

To solve the problem, we need to analyze the forces acting on the electron when it is projected in the presence of both electric and magnetic fields that are aligned in the same direction.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- The electron is negatively charged and is projected in the same direction as both the electric field (E) and the magnetic field (B).
- The force due to the electric field (F_E) acting on the electron can be calculated using the formula:
\[ F_E = qE \]
where \( q \) is the charge of the electron (which is negative).

2. **Electric Force Direction**:
- Since the charge of the electron is negative, the direction of the electric force will be opposite to the direction of the electric field. Therefore, if the electric field is directed to the right, the electric force will act to the left.

3. **Magnetic Force Calculation**:
- The magnetic force (F_B) acting on the electron can be calculated using the formula:
\[ F_B = q(\mathbf{v} \times \mathbf{B}) \]
where \( \mathbf{v} \) is the velocity of the electron and \( \mathbf{B} \) is the magnetic field.
- Since the velocity of the electron is in the same direction as the magnetic field, the cross product \( \mathbf{v} \times \mathbf{B} \) will be zero. Thus, the magnetic force acting on the electron is:
\[ F_B = 0 \]

4. **Net Force on the Electron**:
- The only force acting on the electron is the electric force, which is directed opposite to its motion. Therefore, the net force acting on the electron is:
\[ F_{net} = F_E + F_B = F_E + 0 = F_E \]

5. **Effect on the Electron's Motion**:
- Since the net force is acting in the opposite direction to the velocity of the electron, it will cause the electron to decelerate. The speed of the electron will decrease over time due to the electric force acting against its motion.

6. **Conclusion**:
- The electron will not be deflected because there is no magnetic force acting on it. Instead, it will experience a decrease in speed due to the electric force acting in the opposite direction.

### Final Answer:
The electron will decelerate (its speed will decrease) but will not be deflected.

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